Physics Chapter 3
B
1) If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude. A) True B) False
D
10) The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is A) 0° B) 90° C) 270° D) 180° E) 360°
B
103) A projectile is fired from the edge of a cliff as shown in the figure. The initial velocity components are 940 m/s (horizontal) and 96 m/s (vertical). The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. How high is point P above point Q, assuming no air resistance? A) 470 m B) 490 m C) 45,000 m D) 940 m E) 90,000 m
A
104) As shown in the figure, a projectile is fired at time t = 0.00 s, from point 0 at the upper edge of a cliff, with initial velocity components of and The projectile rises and then falls into the sea at point P. The time of flight of the projectile is and air resistance is negligible. At this location, g = 9.80 m/s2. What is the horizontal distance D? A) 2250 m B) 2520 m C) 2790 m D) 3060 m E) 3330 m
D
105) A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal. Neglecting air resistance, what is horizontal component of the projectile's acceleration? A) 80 m/s2 B) 40 m/s2 C) 9.8 m/s2 D) 0 m/s2 E) 69 m/s2
C
106) A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. If we neglect air resistance, the magnitude of the acceleration of the ball while it is in flight is A) 25 m/s2. B) 18 m/s2. C) 9.8 m/s2. D) 8.5 m/s2. E) 0 m/s2.
D
107) A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance, A) its range will be increased by . B) its range will double. C) its range will be decreased by a factor of two. D) its range will quadruple. E) its range will decrease by a factor of four.
A
108) A hobbyist launches a projectile from ground level on a horizontal plain. It reaches a maximum height of 72.3 m and lands 111 m from the launch point, with no appreciable air resistance. What was the angle of launch if g = 9.80 m/s2? A) 69.0° B) 67.4° C) 22.6° D) 44.8°
B
109) You are traveling at 55 mi/h along the +x-axis relative to a straight, level road and pass a car that is traveling at 45 mi/h. The relative velocity of your car to the other car is A) -10 mi/h. B) 10 mi/h. C) 65 mi/h. D) 35 mi/h.
A
11) A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity? A) 18.1 m/s B) 15.6 m/s C) 8.45 m/s D) 12.6 m/s E) 9.33 m/s
C
11) Vectors and obey the equation + = 0. These vectors satisfy which one of the following statements? A) Vectors and are at right angles to each other. B) Vectors and point in the same direction. C) Vectors and have the same magnitudes. D) The magnitude of is the negative of the magnitude of .
A
110) Your motorboat can move at 30 km/h in still water. What is the minimum time it will take you to move 12 km downstream in a river flowing at 6.0 km/h? A) 20 min B) 22 min C) 24 min D) 30 min
C
112) A plane has an airspeed of 200 m/s northward, and is in a wind of 50.0 m/s to the west. The plane's speed relative to the ground is A) 150 m/s. B) 200 m/s. C) 206 m/s. D) 250 m/s.
B
113) An airplane with an airspeed of 120 km/h has a heading of 30° east of north in a wind that is blowing toward the west at 30 km/h. What is the speed of the plane relative to the ground? A) 90 km/h B) 110 km/h C) 140 km/h D) 150 km/h
A
114) A plane moving 200 m/s horizontally fires a projectile with speed 50 m/s in a forward direction 30.0° below the horizontal. At that instant, what is the speed of the projectile with respect to a stationary observer on the ground? A) 245 m/s B) 250 m/s C) 268 m/s D) 293 m/s
B
116) On a calm day with no wind, you can run a 1500-m race at a velocity of 4.0 m/s. If you run the same race on a day when you have a constant headwind that slows your speed by 2.0 m/s, how much time would it take you to finish the race? A) 250 s B) 750 s C) 1125 s D) 9000 s
A
12) The magnitude of is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 ° with the +y-axis. The components of are closest to: A) = -3.1 m, = 4.6 m. B) = 3.1 m, = -4.6 m. C) = 4.6 m, = -3.1 m. D) = -4.6 m, = 3.1 m. E) = -4.6 m, = -3.1 m.
A
122) A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is A) 157 m/s at an angle 7.31° south of east. B) 157 m/s at an angle 7.31° east of south. C) 155 m/s at an angle 7.36° south of east. D) 155 m/s at an angle 7.36° east of south. E) 157 m/s at an angle 7.36° south of east.
D
123) A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the heading of the plane in order to move directly eastward relative to the ground? A) 78.1° north of east B) 11.9° north of east C) 77.8° north of east D) 12.2° north of east E) 55.3° north of east
D
124) A plane has an airspeed of 142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity? A) 130 m/s B) 16 m/s C) 160 m/s D) 141 m/s E) 48 m/s
A
125) An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the point of origin of the flight. The plane flies with an airspeed of 120 m/s. If a constant wind blows at 10 m/s toward the west during the flight, what direction must the plane fly relative to the air to arrive at the destination? A) 4.8° east of north B) 5.9° east of north C) 85° west of north D) 4.8° west of north E) 5.9° west of north
A
126) A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. How fast can she swim in still water? A) 0.50 m/s B) 0.80 m/s C) 1.2 m/s D) 1.4 m/s E) 1.8 m/s
C
127) A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. What is the speed of the current? A) 0.50 m/s B) 0.80 m/s C) 1.2 m/s D) 1.4 m/s E) 1.8 m/s
D
129) A boat, whose speed in still water is 8.0 m/s, crosses a river with a current of 6.0 m/s. If the boat heads perpendicular to the current, what is the speed of the boat relative to an observer standing on the shore as it crosses the river? A) 5.3 m/s B) 6.0 m/s C) 8.0 m/s D) 10.0 m/s
A
13) The components of vectors and are given as follows: = -9.2 = -4.5 = -6.1 = 4.3 The angle (less than 180°) between vectors and is closest to A) 77°. B) 103°. C) 10°. D) 170°. E) 84°.
A
130) A plane flies directly from city A to city B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes less than the trip from A to B. What is the airspeed (assumed constant) of the plane relative to the air (that is, the airspeed)? A) 530 mi/h B) 400 mi/h C) 480 mi/h D) 610 mi/h
A
131) The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes 0.53 s for it to reach the floor. What is the mass m of the block on the left? There is no friction or mass in the pulley, and the connecting rope is very light. A) 16 kg B) 14 kg C) 13 kg D) 11 kg
C
133) In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B is gently released from rest, how long does it take block B to travel 80.0 cm? A) 0.404 s B) 0.494 s C) 0.639 s D) 0.785 s E) 0.935 s
B
135) The coefficients of static and kinetic friction between a 3.0-kg box and a horizontal desktop are 0.40 and 0.30, respectively. What is the force of friction on the box when a 15-N horizontal push is applied to the box? A) 12 N B) 8.8 N C) 15 N D) 6.0 N E) 4.5 N
A
136) An object slides on a level floor. It slows and comes to a stop with a constant acceleration of magnitude 2.4 m/s2. What is the coefficient of kinetic friction between the object and the floor? A) 0.24 B) 0.48 C) 0.12 D) It is impossible to determine without knowing the mass of the object.
B
138) A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance between the point that the driver slammed on the brakes (thereby locking the wheels) and the point where the car came to a stop was 28.0 m. From a reference manual he determines that the coefficient of kinetic friction between the tires and the road under the prevailing conditions was 0.300. How fast was the car going when the driver applied the brakes? A) 10.7 m/s B) 12.8 m/s C) 21.4 m/s D) 32.9 m/s E) 45.7 m/s
D
139) A 50-kg box is being pushed along a horizontal surface. The coefficient of static friction between the box and the ground is 0.65, and the coefficient of kinetic friction is 0.35. What horizontal force must be exerted on the box for it to accelerate at 1.2 m/s2? A) 60 N B) 120 N C) 170 N D) 230 N E) 490 N
C
14) A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector? A) 0 km B) 20 km C) 28 km D) 40 km
C
140) A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 30.0° below the horizontal is applied to the box. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.30. What is the force of friction on the box? A) 32 N B) 200 N C) 220 N D) 250 N E) 620 N
B
141) A baseball player is running to second base at 5.03 m/s. When he is 4.80 m from the plate he goes into a slide. The coefficient of kinetic friction between the player and the ground is 0.180, and the coefficient of static friction is 3.14. What is his speed when he reaches the plate? A) 4.47 m/s B) 2.89 m/s C) 1.96 m/s D) 2.56 m/s E) He stops before reaching the plate.
B
15) If a vector's components are all negative, then the magnitude of the vector is negative. A) True B) False
A
15) You walk to the north, then turn 60° to your right and walk another How far are you from where you originally started? A) 68 m B) 39 m C) 75 m D) 35 m
A
16) The magnitude of a vector can never be less than the magnitude of any of its components. A) True B) False
A
16) You walk 53 m to the north, then you turn 60° to your right and walk another Determine the direction of your displacement vector. Express your answer as an angle relative to east. A) 63° N of E B) 50° N of E C) 57° N of E D) 69° N of E
A
17) The components of vectors and are given as follows: Ax = 7.6 Bx = -5.1 Ay = -9.2 By = -6.8 What is the magnitude of the vector difference - ? A) 13 B) 3.5 C) 16 D) 170 E) 3.4
A
17) The magnitude of a vector an only zero if all of its components are zero. A) True B) False
B
18) If a vector has components Ax < 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90° B) 90° to 180° C) 180° to 270° D) 270° to 360° E) It cannot be determined without additional information.
D
18) If vector has components Ax = -3.0 lb and Ay = -4.0 lb, and vector has components Bx = 3.0 lb and By = -8.0 lb, what is the magnitude of vector = - ? A) 13 lb B) 16 lb C) 140 lb D) 7.2 lb
C
19) If a vector has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90° B) 90° to 180° C) 180° to 270° D) 270° to 360° E) cannot be determined without additional information
A
19) Vector has magnitude 2 units and is directed to the north. Vector has magnitude and is directed to the south. Calculate the magnitude and direction of A) 7 units, north B) 7 units, south C) 3 units, north D) 3 units, south
D
2) The x component of vector is 8.7 units, and its y component is -6.5 units. The magnitude of is closest to A) 9.9 units B) 7.9 units C) 8.9 units D) 11 units E) 12 units
B
2) Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum A) is equal to 2.0 m. B) could be as small as 2.0 m or as large as 12 m. C) is equal to 12 m. D) is equal to 8.6 m.
D
20) If a vector has components Ax > 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90° B) 90° to 180° C) 180° to 270° D) 270° to 360° E) cannot be determined without additional information
C
20) Two perpendicular vectors, and , are added together giving vector . If the magnitudes of both vectors and are doubled without changing their directions, the magnitude of vector will A) increase by a factor of 8. B) increase by a factor of 4. C) increase by a factor of 2. D) increase by a factor of . E) not change.
D
21) The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements must be correct for these two vectors? A) Vector is parallel to vector . B) Vector is antiparallel (in the opposite direction) to vector . C) Vector must be perpendicular to vector . D) The magnitude of vector must be equal to the magnitude of vector . E) The angle between vector and vector must be 90°.
D
22) Vector is along the +x-axis and vector is along the +y-axis. Which one of the following statements is correct with respect to these vectors? A) The x component of vector is equal to the x component of vector . B) The y component of vector is equal to the y component of vector . C) The x component of vector is equal to the y component of vector . D) The y component of vector is equal to the x component of vector .
B
23) Shown below are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to its right?
A
24) A boulder rolls off of a very high cliff and experiences no significant air resistance. While it is falling, its trajectory is never truly vertical. A) True B) False
B
25) For general projectile motion with no air resistance, the horizontal component of a projectile's velocity A) remains zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) first decreases and then increases.
A
25) Vector = 4.00 m points eastward and vector = 3.00 m points southward. The resultant vector + is given by A) 5.00 m at an angle of 36.9° south of east. B) 5.00 m at an angle of 53.1° south of east. C) 5.00 m at an angle of 71.6° south of east. D) 5.00 m at an angle of 18.4° south of east. E) 5.00 m at an angle of 26.6° south of east.
A
26) For general projectile motion with no air resistance, the horizontal component of a projectile's acceleration A) is always zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) first decreases and then increases.
D
26) Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° east of north. The resultant vector + is given by A) 0.70 m at an angle of 42° north of east. B) 14 m at an angle of 42° north of east. C) 1.1 m at an angle of 42° north of east. D) 9.7 m at an angle of 42° north of east. E) 2.0 m at an angle of 42° north of east.
B
27) For general projectile motion with no air resistance, the vertical component of a projectile's acceleration A) is always zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) first decreases and then increases.
C
27) Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° west of north. The resultant vector + is given by A) 9.8 m at an angle of 64° east of north. B) 9.8 m at an angle of 26° north of east. C) 7.2 m at an angle of 26° east of north. D) 3.3 m at an angle of 26° north of east. E) 3.3 m at an angle of 64° east of north.
D
28) Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° west of south. The resultant vector + is given by A) 2.7 m at an angle of 8.3° south of east. B) 2.7 m at an angle of 8.3° east of south. C) 3.2 m at an angle of 8.3° east of south. D) 3.2 m at an angle of 8.3° south of east. E) 2.3 m at an angle of 8.3° south of east.
E
28) Which of the following statements are true about an object in two-dimensional projectile motion with no air resistance? (There could be more than one correct choice.) A) The speed of the object is constant but its velocity is not constant. B) The acceleration of the object is +g when the object is rising and -g when it is falling. C) The acceleration of the object is zero at its highest point. D) The speed of the object is zero at its highest point. E) The horizontal acceleration is always zero and the vertical acceleration is always a non-zero constant downward.
C
29) A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance? A) It is impossible to tell because we do not know their masses. B) the stone C) the ball D) Both are traveling at the same speed.
A
29) Vector has a magnitude of 6.0 m and points 30° south of east. Vector has a magnitude of 4.0 m and points 30° west of south. The resultant vector + is given by A) 7.2 m at an angle of 64° south of east. B) 3.3 m at an angle of 64° south of east. C) 9.8 m at an angle of 26° south of east. D) 9.8 m at an angle of 64° south of east. E) 3.3 m at an angle of 26° south of east.
C
3) Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant? A) 10 mm B) 20 mm C) 40 mm D) 80 mm
A
3) When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was 1.8 m/s. What was the angle of the mountain surface above the horizontal? A) 75° B) 57 ° C) 33° D) 15°
C
30) In an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble is dropped from the same height. Compare the times of fall of the two pebbles. A) The thrown pebble hits first. B) The dropped pebble hits first. C) They hit at the same time. D) We cannot tell without knowing which pebble is heavier.
D
30) Vector has a magnitude of 4.0 m and points 30° south of east. Vector has a magnitude of 2.0 m and points 30° north of west. The resultant vector + is given by A) 10.0 m at an angle 30° south of east. B) 10.0 m at an angle 60° east of south. C) 2.0 m at an angle 60° south of east. D) 2.0 m at an angle 30° south of east. E) 1.0 m at an angle 30° east of south.
B
31) A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will A) be behind the package. B) be directly over the package. C) be in front of the package. D) depend on the speed of the plane when the package was released.
D
31) Vector has a magnitude of 7.0 m and points 30° east of north. Vector has a magnitude of 5.0 m and points 30° west of south. The resultant vector + is given by A) 10.0 m at an angle 60° north of east. B) 10.0 m at an angle 30° east of north. C) 2.0 m at an angle 30° north of east. D) 2.0 m at an angle 60° north of east. E) 1.0 m at an angle 60° east of north
B
32) James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. If there is no air resistance, when they reach the lake below A) the splashdown speed of James is larger than that of John. B) the splashdown speed of John is larger than that of James. C) they will both have the same splashdown speed. D) the splashdown speed of James must be 9.8 m/s larger than that of John. E) the splashdown speed of John must be 25 m/s larger than that of James.
B
32) Vector has a magnitude of 6.0 m and points 30° east of south. Vector has a magnitude of 4.0 m and points 30° west of north. The resultant vector + is given by A) 2.0 m at an angle of 30° north of west. B) 2.0 m at an angle of 30° east of south. C) 10.0 m at an angle of 60° north of west. D) 10.0 m at an angle of 60° east of south. E) 1.0 m at an angle of 60° north of west.
C
33) James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. Compare the time it takes each to reach the lake below if there is no air resistance. A) James reaches the surface of the lake first. B) John reaches the surface of the lake first. C) James and John will reach the surface of the lake at the same time. D) Cannot be determined without knowing the mass of both James and John. E) Cannot be determined without knowing the weight of both James and John.
D
33) Vector has a magnitude of 8.0 m and points east, vector has a magnitude of 6.0 m and points north, and vector has a magnitude of 5.0 m and points west. The resultant vector + + is given by A) 2.0 m at an angle 63° north of east. B) 2.0 m at an angle 63° east of north. C) 6.7 m at an angle 63° east of north. D) 6.7 m at an angle 63° north of east. E) 3.8 m at an angle 67° north of east
B
34) A player kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory A) both the velocity and the acceleration of the soccer ball are zero. B) neither the ball's velocity nor its acceleration are zero. C) the ball's acceleration is zero but its velocity is not zero. D) the ball's acceleration points upward. E) the ball's velocity points downward.
C
34) The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to A) 19 B) 16 C) 13 D) 10 E) 7.0
C, E
35) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the following statements are true about just as the snowballs reach the ground below? (There could be more than one correct choice.) A) Debra's snowball will have a higher speed than Mary's snowball. B) Mary's snowball will have a higher speed than Debra's snowball. C) Both snowballs will hit the ground with the same speed. D) Both snowballs hit the ground at the same time. E) Mary's snowball reaches the ground before Debra's snowball.
A, D
36) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the following statements are true about just before the snowballs reach the ground below? (There could be more than one correct choice.) A) Debra's snowball will stay in the air longer than Mary's snowball. B) Mary's snowball will stay in the air longer than Debra's snowball. C) Both snowballs will take the same amount of time to hit the ground. D) Debra's snowball has exactly the same acceleration as Mary's snowball. E) Mary's snowball has a greater downward acceleration than Debra's snowball.
D
37) A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which of the following statements about the rock's motion are true just before it hits the ground? (There could be more than one correct choice.) A) Its horizontal velocity component is zero. B) Its velocity is vertical. C) Its vertical velocity component is the same as it was just as it was launched. D) Its horizontal velocity component is the same as it was just as it was launched. E) Its speed is the same as it was just as it was launched.
A
37) An airplane undergoes the following displacements, all at the same altitude: First, it flies in a direction 30.0° east of north. Next, it flies due south. Finally, it flies 30.0° north of west. Use components to determine how far the airplane ends up from its starting point. A) 71.5 km B) 73.0 km C) 74.4 km D) 70.1 km E) 68.7 km
D
38) You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat A) directly toward the west. B) directly toward the north. C) in a general southwesterly direction. D) in a general northwesterly direction.
E
39) Three forces, 1, 2, and 3, each of magnitude 70 N, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is A) 35 N. B) 70 N. C) 140 N. D) 210 N. E) 0 N.
C
39) You push on box G that is next to box H, causing both boxes to slide along the floor, as shown in the figure. The reaction force to your push is A) the push of box G on box H. B) the push of box H on box G. C) the push of box G against you. D) the upward force of the floor n box G. E) the acceleration of box G.
B
4) The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors. A) True B) False
A
4) When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity? A) 4.8 m/s B) 4.3 m/s C) 3.8 m/s D) 3.4 m/s
C
40) A small car and a large SUV are at a stoplight. The car has a mass equal to half that of the SUV, and the SUV can produce a maximum accelerating force equal to twice that of the car. When the light turns green, both drivers push their accelerators to the floor at the same time. Which vehicle pulls ahead of the other vehicle after a few seconds? A) The car pulls ahead. B) The SUV pulls ahead. C) It is a tie.
D
40) Three forces, 1, 2, and 3, all act on an object, as shown in the figure. The magnitudes of the forces are: F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N. The resultant force acting on the object is given by A) 180 N at an angle of 60.0° with respect to +x-axis. B) 60.0 N at an angle of 90.0° with respect to +x-axis. C) 20.0 N at an angle of 34.3° with respect to +x-axis. D) 35.5 N at an angle of 34.3° with respect to +x-axis. E) 40.0 N at an angle of 60.0° with respect to +x-axis.
D
41) An object is moving with constant non-zero velocity. Which of the following statements about it must be true? A) A constant force is being applied to it in the direction of motion. B) A constant force is being applied to it in the direction opposite of motion. C) A constant force is being applied to it perpendicular to the direction of motion. D) The net force on the object is zero. E) Its acceleration is in the same direction as it velocity.
D
41) Four vectors, , , , and , are shown in the figure. The sum of these four vectors is a vector having magnitude and direction A) 4.0 cm, along +x-axis. B) 4.0 cm, along -x-axis. C) 4.0 cm, along +y-axis. D) 4.0 cm, along -y-axis. E) 4.0 cm, 45° above +x-axis.
B
42) A 20-ton truck collides with a 1500-lb car. Which of the following statements must be true? A) During the collision, the force on the truck is greater then the force on the car. B) During the collision, the force on the truck is equal to the force on the car. C) During the collision, the force on the truck is smaller than the force on the car. D) The truck did not slow down during the collision, but the car did. E) The car did not slow down during the collision, but the truck did.
D
42) Vector has a magnitude of 8.0 m and points 30° north of east; vector has a magnitude of 6.0 m and points 30° west of north; and vector has a magnitude of 5.0 m and points 30° west of south. The resultant vector + + is given by A) 2.7 m at an angle 74° north of east. B) 5.9 m at an angle 74° north of east. C) 4.8 m at an angle 74° east of north. D) 5.1 m at an angle 74° north of east. E) 2.1 m at an angle 66° east of north.
A
45) The figure shows four vectors, , , , and , having magnitudes 12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is A) 16.4 m at an angle 77.8° with respect to +x-axis. B) 16.4 m at an angle 12.3° with respect to +x-axis. C) 19.5 m at an angle 77.8° with respect to +x-axis. D) 19.5 m at an angle 12.3° with respect to +x-axis. E) 8.20 m at an angle 77.8° with respect to +x-axis.
Between 7.0 m and 17.0 m
5) A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?
A
5) The x component of vector is 5.3 units, and its y component is -2.3 units. The angle that vector makes with the +x-axis is closest to A) 340° B) 160° C) 250° D) 110° E) 23°
E
50) Three vectors, , , and , have the components shown in the table. What is the magnitude of the resultant of these three vectors? x component y component 3.50 m -4.50 m 2.00 m 0.00 m -5.50 m 2.50 m A) 5.50 m B) 13.0 m C) 11.1 m D) 7.00 m E) 2.00 m
D
51) Three vectors, , , and , have the components shown in the table. What angle does the resultant of these three vectors make with the +x-axis? x component y component -3.5 m 4.5 m 0.00 m -6.5 m 5.5 m -2.5 m A) 24° above the +x-axis B) 24° below the +x-axis C) 66° above the +x-axis D) 66° below the +x-axis
A
54) A ball is thrown with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact top of its trajectory? A) 10 m/s B) 17 m/s C) 20 m/s D) zero
B
55) A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level? A) 4.0 m/s B) 8.0 m/s C) 16 m/s D) 9.8 m/s
D
56) A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff if air resistance is negligibly small? A) 22 m B) 43 m C) 77 m D) 91 m
C
57) A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance? A) 14 m B) 16 m C) 20 m D) 24 m
C
58) A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance? A) 6.1 m/s B) 7.4 m/s C) 8.1 m/s D) 8.9 m/s
B
6) If + = and their magnitudes are given by A + B = C, then the vectors and are oriented A) perpendicular relative to one other. B) parallel to each other (in the same direction). C) antiparallel to each other (in opposite directions). D) It is impossible to know from the given information.
D
60) The acceleration due to gravity on the Moon is only one-sixth of that on Earth, and the Moon has no atmosphere. If you hit a baseball on the Moon with the same effort (and therefore at the speed and angle) as on Earth, how far would the ball would travel on the Moon compared to on Earth? Neglect air resistance on Earth. A) 1/6 as far as on Earth B) 36 times as far as on Earth C) the same distance as on Earth D) 6 times as far as on Earth E) as far as on Earth
A
61) A boy throws a rock with an initial velocity of 3.13 m/s at 30 degrees about the horizontal. How long does it take for the rock to reach the maximum height of its trajectory? A) 0.160 s B) 0.282 s C) 0.313 s D) 0.441 s
A
62) A cat leaps to try to catch a bird. If the cat's jump was at 60° off the ground and its initial velocity was 2.74m/s. what is the highest point of its trajectory, neglecting air resistance? A) 0.29 m B) 0.58 m C) 10.96 m D) 0.19 m
A
63) A fisherman casts his bait toward the river at an angle of 25° above the horizontal. As the line unravels, he notices that the bait and hook reach a maximum height of 2.9m. What was the initial velocity he launched the bait with? Assume that the line exerts no appreciable drag force on the bait and hook and that air resistance is negligible. A) 18 m/s B) 7.9 m/s C) 7.6 m/s D) 6.3 m/s
A
64) A football kicker is attempting a field goal from 44m out. The ball is kicked and just clears the lower bar with a time of flight of 2.9 s. If the angle of the kick was 45°, what was the initial speed of the ball, assuming no air resistance? A) 21.5 m/s B) 19.7 m/s C) 2.2 m/s D) 39 m/s
A
65) You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance. After 2.0 s, the magnitude of the velocity of the rock is closest to A) 28 m/s B) 20 m/s C) 40 m/s D) 37 m/s
D
7) A displacement vector is 34.0 m in length and is directed 60.0° east of north. Selecting from the choices in the table below, what are the components of this vector? Northward Eastward choice component component 1 29.4 m 17.0 m 2 18.2 m 28.1 m 3 22.4 m 11.5 m 4 17.0 m 29.4 m 5 25.2 m 18.2 m A) choice 1 B) choice 2 C) choice 3 D) choice 4 E) choice 5
A
7) If - = 0, then the vectors and have equal magnitudes and are directed in the same direction. A) True B) False
A
75) A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally. The height of the platform above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect air resistance. A) 21 m/s B) 22 m/s C) 24 m/s D) 25 m/s E) 6.3 m/s
B
76) A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally and experiences no significant air resistance. The height of the platform above the ground is 2.0 m. What is the magnitude of the vertical component of the velocity of the puck just before it hits the ground? A) 20 m/s B) 6.3 m/s C) 13 m/s D) 15 m/s E) 21 m/s
D
77) A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/shorizontally in a city where the acceleration due to gravity is 9.81 m/s2. The puck experiences no significant air resistance as it falls. The height of the platform above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground? A) 77.2° B) 72.6° C) 12.8° D) 12.6° E) 31.8°
A
78) A plane flying horizontally at a speed of 50 m/s and at an elevation of 160 m drops a package, and 2.0 s later it drops a second package. How far apart will the two packages land on the ground if air resistance is negligible? A) 100 m B) 160 m C) 180 m D) 320 m
B
79) In a room where g = 9.81 m/s2, a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally. The height of the platform above the ground is 2.00 m. What is the speed of the puck just before it hits the ground? The air resistance is negligibly small. A) 48.2 m/s B) 28.7 m/s C) 28.0 m/s D) 26.3 m/s E) 6.26 m/s
E
8) A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football? A) 64.7m B) 55.0 m C) 0.00 m D) 74.0 m E) 24.2 m
B
8) If three vectors add to zero, they must all have equal magnitudes. A) True B) False
A
80) A ball rolls over the edge of a platform with only a horizontal velocity. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the horizontal velocity of the ball just before it touches the ground? Neglect air resistance. A) 35 m/s B) 9.8 m/s C) 20 m/s D) 4.9 m/s E) 70 m/s
D
82) A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s2. A) 202 m/s B) 9.80 m/s C) 19.6 m/s D) 45.2 m/s E) 94.4°
E
83) A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m, as shown in the figure. The width of the pylon is very narrow, and the length of each propeller blade is 12 m. A tip of the propeller breaks off just when the propeller is vertical. The fragment flies off horizontally, falls, and strikes the ground at point P with negligible air resistance. Just before the fragment broke off, the propeller was turning uniformly, taking 1.2 s for each rotation. How far is point P from the base of the pylon? A) 120 m B) 130 m C) 140 m D) 150 m E) 160 m
A
84) A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal. If air resistance is negligible, how high above the projection point is the ball after 2.0 s? A) 5.4 m B) 13 m C) 25 m D) 43 m E) 50 m
C
85) A projectile is fired from ground level with a speed of 150 m/s at an angle 30° above the horizontal on an airless planet where g = 10.0 m/s2. What is the horizontal component of its velocity after 4.0 s? A) 150 m/s B) 35 m/s C) 130 m/s D) 75 m/s E) 38 m/s
B
86) A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal. What is the vertical component of its velocity after 4.0 s if air resistance is neglected? A) 150 m/s B) 36 m/s C) 130 m/s D) 75 m/s E) 38 m/s
B
88) A child is trying to throw a ball over a fence. She gives the ball an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground and the fence is 2.0 m high. The ball just clears the fence while still traveling upwards and experiences no significant air resistance. How far is the child from the fence? A) 0.73 m B) 1.6 m C) 2.7 m D) 3.8 m E) 7.5 m
B
89) A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the horizontal distance to the point where the football hits the ground if we neglect air resistance? A) 20 m B) 35 m C) 18 m D) 60 m E) 30.0 m
D
9) The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is A) 90° B) 180° C) 60° D) 0° E) 270°
B
90) An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 55° with the vertical. What is the length of the athlete's jump if air resistance is of no significance? A) 0.88 m B) 8.0 m C) 12 m D) 17 m E) 4.0 m
C
91) An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 35° above the horizontal. How long does the athlete stay in the air, assuming no significant air resistance? A) 0.50 s B) 0.88 s C) 1.1 s D) 2.5 s E) 0.54 s
C
92) An athlete participates in an interplanetary discus throw competition during an Olympiad that takes place on a planet where the acceleration due to gravity is 9.7 m/s2. He throws the discus with an initial velocity of 20 m/s at an angle of 60° from the vertical. Neglecting air resistance and the height of the discus at the point of release, what is the range of the discus? A) 21 m B) 60 m C) 36 m D) 40 m E) 32 m
C
94) A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground. At what angle below the horizontal does the ball approach the ground? A) 35° B) 42° C) 48° D) 40° E) 65°
B
95) The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively. If there is no air resistance, how long does it take the football to reach the top of its trajectory? A) 1.0 s B) 2.0 s C) 3.0 s D) 4.0 s E) 5.0 s
C
96) A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what angle was the projectile fired above the horizontal? A) 45° B) 60° C) 30° D) 90° E) 75°
B
97) A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before the projectile hits the level ground? A) 5.00 seconds B) 10.0 seconds C) 15.0 seconds D) 20.0 seconds
