Physics Test 1
At time t = 0 s, an object is observed at x = 0 m; and its position along the x axis follows this expression: x = 4t + t2, where the units for distance and time are meters and seconds, respectively. What is the object's displacement x between t = 1.0 s and t = 3.0 s? (Practice Test 1 #11)
+16m 4t+t^2 4(3) + (3)^2= 21 21-5 =16
A brass ball is shot vertically upward from the surface of an atmosphere-free planet with an initial speed of 20.0 m/s. One second later, the ball has an instantaneous velocity in the upward direction of 15.0 m/s. Determine the velocity of the ball when it returns to its original position. Note: assume the upward direction is positive (Practice Test 1 #20)
-20m/s
A honeybee leaves the hive and travels a total distance of 2 km before returning to the hive. What is the magnitude of the displacement vector of the bee? (2.1)
0 km
A rocket is fired at a speed of 60.0 m/s from ground level, at an angle of 53.0° above the horizontal. The rocket is fired toward an 33.7-m high wall, which is located 33.0 m away. The rocket attains its launch speed in a negligibly short period of time, after which its engines shut down and the rocket coasts. By how much does the rocket clear the top of the wall? (Ch 3 #10)
000
Given the quantities a = 8.4 m, b = 2.3 s, c = 94 m/s, what is the value of the quantity d = (a^3)/(cb^2) ? (Ch 1 #6)
1.20 m^2/s --8.4^3 / 69(4.2)^2
A train with a constant speed of 16 m/s passes through a town. After leaving the town, the train accelerates at 0.33 m/s2 until it reaches a speed of 35 m/s. How far did the train travel while it was accelerating? (Practice Test 1 #9)
1.5 km 35^2 - 16^2 =2(0.33)x x= 1.5 km
The velocity of a train is 80.0 km/h, due west. One and a half hours later its velocity is 65.0 km/h, due west. What is the train's average acceleration? (Ch 2 #2)
10.0 km/h2, due east
A train with a constant velocity of +28.6 m/s approaches a small town . The operator applies the brake, reducing the train's velocity to +11.4 m/s. If the average acceleration of the train during braking is -1.35 m/s2, for what elapsed time does the operator apply the brake? (Practice Test 1 #5)
12.7 s 11.4 = 28.6 - 1.35 * t
Ryan throws a tennis ball vertically upward. The ball returns to the point of release after 3.5 s. What is the speed of the ball as it is released? (Practice Test 1 #13)
17 m/s (9.8)(3.5)^2 / (2)(3.5) = 17
A student sees a newspaper ad for an apartment that has 2130 square feet (ft2) of floor space. How many square meters of area are there? (Ch 1 #5)
197.88 m^2 --1 ft = 0.3048 m --2130 x 0.3048 x 0.3048
A brick is dropped from rest from a height of 4.9 m. How long does it take the brick to reach the ground? (Practice Test 1 #12)
1s
An arrow is shot horizontally from a height of 4.9 m above the ground. The initial speed of the arrow is 45 m/s. Neglecting friction, how long will it take the arrow to hit the ground? (Practice Test 1 #30)
1s
A ball is thrown straight upward with a velocity v0 and in a time t reaches the top of its flight path, which is a displacement y above the launch point. With a launch velocity of 2v0 , what would be the time required to reach the top of its flight path and what would be the displacement of the top point above the launch point? (2.6)
2t and 4y
A turtle takes 3.5 minutes to walk 18 m toward the south along a deserted highway. A truck driver stops and picks up the turtle. The driver takes the turtle to a town 1.1 km to the north with an average speed of 12 m/s. What is the magnitude of the average velocity of the turtle for its entire journey? (Practice Test 1 #2)
3.6 m/s
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. What is the speed of the projectile when it is at the highest point in its trajectory? (Practice Test 1 #26)
30m/s
During a relay race, runner A runs a certain distance due north and then hands off the baton to runner B, who runs for the same distance in a direction south of east. The two displacement vectors A and B can be added together to give a resultant vector R. Which drawing correctly shows the resultant vector? (Ch 1 #1)
4
Each drawing shows three points along the path of a projectile, one on its way up, one at the top, and one on its way down. The launch point is on the left in each drawing. Which drawing correctly represents the acceleration a of the projectile at these three points? (Ch 3 #1)
4
A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. What is the magnitude of the horizontal component of the projectile's displacement at the end of 2 s? (Practice Test 1 #21)
40 m 2(35cos55o) = 40m
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. Approximately how long does it take the projectile to reach the highest point in its trajectory? (Practice Test 1 #25)
4s
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. What is the magnitude of the projectile's velocity just before it strikes the ground? (Practice Test 1 #28)
50 m/s
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. At what angle is the projectile fired (measured with respect to the horizontal)? (Practice Test 1 #24)
53*
The two hot-air balloons in the drawing are 48.2 m and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3° above the horizontal. What is the horizontal distance x between the two balloons? (Ch 1 #8)
54.2 m --61.0 - 48.2 = 12.8 --tan (13.3) = 12.8 / x --x = 54.2
A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 6.96 m/s. The car is a distance d away. The bear is 36.3 m behind the tourist and running at 10.6 m/s. The tourist reaches the car safely. What is the maximum possible value for d? (Ch 2 #5)
69 m
A car starts from rest and accelerates at a constant rate in a straight line. In the first second the car moves a distance of 2.0 meters. How fast will the car be moving at the end of the second second? (Practice Test 1 #7)
8 m/s
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. What is the acceleration of the projectile when it reaches its maximum height? (Practice Test 1 #27)
9.8 m/s2, downward
Which of the following displacement vectors (if any) are equal? Variable / Magnitude / Direction A / 100m / 30* north of east B / 100m / 30* south of west C / 50m / 30* south of west D / 100m / 60* east of north (1.7)
A and D
Two balls are launched upward from the same spot at different angles with respect to the ground. Both balls rise to the same maximum height. Ball A, however, follows a trajectory that has a greater range that that of ball B. Ignoring air resistance, decide which ball, if either, has the greater launch speed. (3.3)
Ball A
What is the slope of a straight line in the velocity versus time graph? (2.7)
average acceleration
Which one of the following is not a vector quantity? (Practice Test 1 #6)
average speed
Two objects are thrown vertically upward, first one, and then, a bit later, the other. Is it (a) possible or (b) impossible that both objects reach the same maximum height at the same instant of time? (2.6)
b) impossible
A rifle, at a height H above the ground, fires a bullet parallel to the ground. At the same instant and at the same height, a second bullet is dropped from rest. In the absence of air resistance, which bullet, if either, strikes the ground first? (3.3)
both bullets
A leopard springs upward at a 45 degree angle and then falls back to the ground. Air resistance is negligible. There exists a point on the leopard's trajectory at which its speed is one-half its initial value. (3.3)
false
On a riverboat cruise, a plastic bottle is accidentally dropped overboard. A passenger on the boat estimates that the boat pulls ahead of the bottle by 5 meters each second. It is possible to conclude that the magnitude of the velocity of the boat with respect to the shore is 5 m/s (3.4)
false
In the SI system, what are the units of measurement for length, mass, and time (1.2)
meters, kilograms, seconds
An object is moving along the x axis. The graph shows its position from the starting point as a function of time. Various segments of the graph are identified by the letters A, B, C, and D. What is the acceleration of the object at t = 7.0 s? (Practice Test 1 #17)
zero m/s^2
Two vectors, A and B, are shown in the drawing and R = A + B. How many of these three vectors have x and y components that are both positive? (1.7)
one
Suppose the vectors A and B in the drawing have magnitudes of 6.0 m and are directed as shown. What are Ax and Bx, the scalar components of A and B along the x axis? (Ch 1 #4)
Ax = -(6.0 m) cos 35° = -4.9 m; Bx = +(6.0 m) cos 35° = +4.9 m
When using the equations of kinematics to solve motion problems, the velocity and acceleration variables will always be positive (2.5)
false
Is the average speed of a vehicle a vector or a scalar quantity? (2.2)
scalar
Is it possible for two quantities to have the same dimensions but different units? (1.3)
Yes
A projectile is fired into the air, and it follows the parabolic path shown in the drawing, landing on the right. There is no air resistance. At any instant, the projectile has a velocity and an acceleration . Which one or more of the drawings could not represent the directions for and at any point on the trajectory? (3.3)
a and c
A jogger runs along a straight and level road for a distance of 8.0 km and then runs back to her starting point. The time for this roundtrip is 2.0 h. Which one of the following is true? (Ch 2 #1)
Her average speed is 8.0 km/h, and her average velocity is 0 km/h.
Suppose you are driving due east, traveling a distance of 1500 m in 2 minutes. You then turn due north and travel the same distance in the same time. What can be said about the average speeds and the average velocities for the two segments of the trip? (3.1)
The average speeds are the same, but the average velocities are different
Vectors A, B , C and satisfy the vector equation A + B = C, and their magnitudes are related by the scalar equation A + B = C. How is vector A oriented with respect to vector B? (1.6)
The directions are the same
A tennis ball is hit upward into the air and moves along an arc. Neglecting air resistance, where along the arc do the minimum and maximum speeds occur? (3.3)
The maximum speed occurs at the lowest point and the minimum occurs at the highest.
An object is thrown upward at an angle Ө above the ground, eventually returning to earth. Which statement is true? (3.3)
The velocity and acceleration are perpendicular only at the top of the trajectory
Physics results in the advancement of modern technologies because of its ability to predict how nature will behave (1.1)
True
Three or more vectors with unequal magnitudes can be added together so their sum is zero (1.6)
True
The three displacement vectors in the drawing have magnitudes of A = 4.25 m, B = 5.93 m, and C = 3.77 m. Find the resultant((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis. (Ch 1 #12)
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A person is jogging along a straight line, and her displacement is denoted by the vector A in the drawings below. Which drawing represents the correct vector components, Ax and Ay, for the vector A? (Ch 1 #3)
3
The magnitude of a vector has doubled, its direction remaining the same. Can you conclude that the magnitude of each component of the vector has doubled? (1.7)
Yes
A runner runs half the remaining distance to the finish line every ten seconds. She runs in a straight line and does not ever reverse her direction. Does her acceleration have a constant magnitude? (2.3)
no
A motorcycle starts from rest and has a constant acceleration. In a time interval t, it undergoes a displacement x and attains a final velocity v. Then t is increased so that the displacement is 3x. In this same increased time interval, what final velocity does the motorcycle attain? (2.4)
square root of 3v
The muzzle velocity of a gun is the velocity of the bullet when it leaves the barrel. The muzzle velocity of one rifle with a short barrel is greater than the muzzle velocity of another rifle that has a longer barrel. In which rifle is the acceleration of the bullet larger? (2.4)
the rifle with the short barrel
Two vectors A and B are added together to give a resultant vector : R:R = A + B. The magnitudes of and are 3 m and 8 m, respectively, but the vectors can have any orientation. What is (a) the maximum possible value and (b) the minimum possible value for the magnitude of R ? (1.6)
(a) 11m (b) 5m
The following table list four variables, along with their units: Variables/Units x/meters(m) v/meters per second(m/s) t/seconds(s) a/meters per seconds squared(m/s^2) (1.3)
(a) x = vt (b) x = vt + 1/2 at^2 (c) v = at (f) t = square root of (2x/a)
Which of the following statements, if any, involves a vector? (1.5)
(b) I walked two miles due north along the beach (d) I jumped off a cliff and hit the water traveling straight down at a speed of 17 miles per hour
Three cars, A, B, and C, are moving along a straight section of a highway. If the velocity of A relative to B is +60 m/s and the velocity of A relative to C is +20 m/s, then what is the velocity of C relative to B? (3.4)
+40 m/s
An object is moving along the x axis. The graph shows its position from the starting point as a function of time. Various segments of the graph are identified by the letters A, B, C, and D. What is the velocity of the object at t = 7.0 s? (Practice Test 1 #16)
-3 m/s
A projectile is fired horizontally with an initial speed of 57 m/s. What are the horizontal and vertical components of its displacement 3.0 s after it is fired? horizontal vertical (Practice Test 1 #29)
170m -44m
A golfer hits a shot to a green that is elevated 2.50 m above the point where the ball is struck. The ball leaves the club at a speed of 19.8 m/s at an angle of 41.0˚ above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands. (Ch 3 #6)
18.52 m/s
An elevator is moving upward with a speed of 11 m/s. Three seconds later, the elevator is still moving upward, but its speed has been reduced to 5.0 m/s. What is the average acceleration of the elevator during the 3.0 s interval? (Practice Test 1 #3)
2.0 m/s2, downward 5-11 = -6 -6/3 = -2
A tennis ball is struck and departs from the racket horizontally with a speed of 29.3 m/s. The ball hits the court at a horizontal distance of 20.7 m from the racket. How far above the court is the tennis ball when it leaves the racket? (Ch 3 #4)
2.44 m
The minimum takeoff speed for a certain airplane is 75 m/s. What minimum acceleration is required if the plane must leave a runway of length 1050 m? Assume the plane starts from rest at one end of the runway. (Practice Test 1 #8)
2.7 m/s^2 (75m/s)^2 / (2)(1050m) = 2.7 m/s^2
A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. How long does it take the projectile to reach the highest point in its trajectory? (Practice Test 1 #22)
2.9 s t = - 28.67 / - 9.8= 2.93
The drawing shows the sum of three displacement vectors, A, B, and C. The resultant vector is labeled R. Which drawing below shows the correct resultant vector for A - B - C? (Ch 1 #2)
3
The drawing shows two cars traveling in different directions with different speeds. Their velocities are: vAG = velocity of car A relative to the Ground = 23.4 m/s, due east vBG = velocity of car B relative to the Ground = 21.0 m/s, due north The driver of car B looks out the window and sees car A. What is the velocity (magnitude and direction) of car A as observed by the driver of car B? In other words, what is the velocityvABof car A relative to car B? (Ch 3 #2)
31.4 m/s 41.9 degrees south of east
A landing airplane makes contact with the runway with a speed of 75.0 m/s and moves toward the south. After 18.5 seconds, the airplane comes to rest. What is the average acceleration of the airplane during the landing? (Practice Test 1 #4)
4.05 m/s2, north 75/18.5 = 4.05
A automotive test driver travels due north in a prototype hybrid vehicle at 30 mi/h for 2 hours. She then reverses her direction and travels due south at 60 mi/h for 1 hour. What is the average speed of the vehicle? (Practice Test 1 #18)
40 m/h
A rock is dropped from rest from a height h above the ground. It falls and hits the ground with a speed of 11 m/s. From what height should the rock be dropped so that its speed on hitting the ground is 22 m/s? Neglect air resistance. (Practice Test 1 #14)
4h
A powerboat, starting from rest, maintains a constant acceleration. After a certain time t, its displacement and velocity are and . At time 2t, what would be its displacement and velocity, assuming the acceleration remains the same? (3.2)
4r and 2v
A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. Determine the initial speed of the projectile. (Practice Test 1 #23)
50 m/s
Suppose a car is traveling at +19.9 m/s, and the driver sees a traffic light turn red. After 0.352 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 4.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light? (Ch 2 #8)
56.54 m
The Space Shuttle travels at a speed of about 8.51 x 103 m/s. The blink of an astronaut's eye lasts about 95.1 ms. How many football fields (length = 91.4 m) does the Space Shuttle cover in the blink of an eye? (Ch 2 #3)
9 (no units)
Ball A is dropped from rest from a window. At the same instant, ball B is thrown downward; and ball C is thrown upward from the same window. Which statement concerning the balls after their release is necessarily true if air resistance is neglected? (Practice Test 1 #10)
All three balls have the same acceleration at any instant.
An experimental vehicle slows down and comes to a halt with an acceleration whose magnitude is 9.80 m/s2. After reversing direction in a negligible amount of time, the vehicle speeds up with an acceleration of 9.80 m/s2. Except for being horizontal, is this motion (a) the same as or (b) different from the motion of a ball that is thrown straight upward, comes to a halt, and falls back to earth? Ignore air resistance (2.6)
a
A stone is thrown horizontally from the top of a cliff and eventually hits the ground below. A second stone is dropped from rest from the same cliff, falls through the same height, and also hits the ground below. Ignore air resistance. Which of the following quantities is or are different for the two cases? (More than one quantity may be different.) (3.3)
displacement and speed just before impact with the ground
An object is moving along the x axis. The graph shows its position from the starting point as a function of time. Various segments of the graph are identified by the letters A, B, C, and D. During which interval(s) is(are) the object moving in the negative x direction? (Practice Test 1 #15)
during B interval only
A plane takes off at St. Louis, flies straight to Denver, and then returns the same way. The plane flies at the same speed with respect to the ground during the entire flight, and there are no head winds or tail winds. Since the earth revolves around its axis once a day, you might expect that the times for the outbound trip and the return trip differ, depending on whether the plane flies against the earth's rotation or with it. Is this expectation true or false? (3.4)
false
One of the following statements is incorrect. (a) The car traveled around the circular track at a constant velocity. (b) The car traveled around the circular track at a constant speed. Which statement is incorrect? (2.2)
statement a
A wrench is accidentally dropped from the top of the mast on a sailboat. Air resistance is negligible. The wrench will hit at the same place on the deck whether the sailboat is at rest or moving with a constant velocity (3.3)
true
The average velocity for a trip has a positive value. It is possible for the instantaneous velocity at a point during the trip to have a negative value. (2.2)
true
A automotive test driver travels due north in a prototype hybrid vehicle at 30 mi/h for 2 hours. She then reverses her direction and travels due south at 60 mi/h for 1 hour. What is the average velocity of the vehicle? (Practice Test 1 #19)
zero mi/h
The figure shows the speed as a function of time for an object in free fall near the surface of the earth The object was dropped from rest in a long evacuated cylinder. What is the numerical value of the slope of the line? (Practice Test 1 #1)
9.8 m/s^2
The tail of a vector is fixed to the origin of an x,y axis system. Originally the vector points along the +x axis and has a magnitude of 12 units. As time passes, the vector rotates counterclockwise. For which of the following rotational angles is the x component of the vector equal to zero? (1.7)
90 and 270
For an object moving with a constant velocity, what is the slope of a straight line in its position versus time graph? (2.7)
velocity
The highest waterfall in the world is Angel Falls in Venezula, with a total drop of 979 m. Write the height of the falls in cm using scientific notation (1.2)
9.79 X 10^4 cm
When can the equations of kinematics be used to describe the motion of an object? (2.5)
They can be used only when the object is undergoing constant acceleration.
A ball is dropped from rest from the top of a building and strikes the ground with a speed vf. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of the second ball is v0 = vf, the same speed with which the first ball eventually strikes the ground. Ignoring air resistance, decide whether the balls cross paths (a) at half the height of the building, (b) above the halfway point, or (c) below the halfway point. (2.6)
b
The acceleration of a projectile is equal to zero when the projectile reaches the top of its trajectory. (3.3)
false
Two buses depart from Chicago, one going to New York and one to San Francisco. Each bus travels at a speed of 30 m/s, so they have equal velocities (2.2)
false
An object moving with a constant acceleration slows down if the acceleration points in the direction opposite to the direction of the velocity. But can an object ever come to a permanent halt if its acceleration truly remains constant? (2.3)
no
At one instant of time, a car and a truck are traveling side by side in adjacent lanes of a highway. The car has a greater velocity than the truck has. Does the car necessarily have the greater acceleration? (2.3)
no
Two vectors with the same magnitude are necessarily equal. (1.7)
Fasle
Two cars are moving in the same direction (the positive direction) on a straight road. The acceleration of each car also points in the positive direction. Car 1 has a greater acceleration than car 2 has. Which one of the following statements is true? (2.3)
In the same time interval, the velocity of car 1 changes by a greater amount than car 2 does
A vector has a component of zero along the x axis of a certain axis system. Does this vector necessarily have a component of zero along the x axis of another (rotated) axis system? (1.8)
No
Can the Pythagorean theorem relationship be applied to the three sides of any triangle? (1.4)
No
In the equation you wish to determine the integer value (1, 2, etc.) of the exponent n. The dimensions of y, a, and t are known. It is also known that c has no dimensions. Can dimensional analysis be used to determine n? (1.3)
No
Is it possible for two quantities to have the same units but different dimensions? (1.3)
No
You can always add two numbers that have the same units (such as 6 meters + 3 meters). Can you always add two numbers that have the same dimensions, such as two numbers that have the dimensions of length [L]? (1.3)
No
In baseball, the pitcher's mound is raised to compensate for the fact that the ball falls downward as it travels from the pitcher toward the batter. If baseball were played on the moon, where would the pitcher's mound have to be? (3.3)
(b) lower than its height on earth
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t = 0 s, the x components of the puck's initial velocity and acceleration are v0x = +7.0 m/s and ax = +7.7 m/s2. The y components of the puck's initial velocity and acceleration are v0y = +8.6 m/s and ay = -1.6 m/s2. Find (a) the magnitude v and (b) the direction θ of the puck's velocity at a time of t = 0.50 s. Specify the direction relative to the +x axis (Ch 3 #5)
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Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 17.0 m, B = 11.0 m, C = 12.0 m, and D = 26.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the direction as a positive (counterclockwise) angle from the +x axis. (Ch 1 #13)
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A cement block accidentally falls from rest from the ledge of a 81.0-m-high building. When the block is 18.0 m above the ground, a man, 1.70 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the way? (Ch 2 #11)
0.44 s
A woman on a bridge 105 m high sees a raft floating at a constant speed on the river below. She drops a stone from rest in an attempt to hit the raft. The stone is released when the raft has 8.66 m more to travel before passing under the bridge. The stone hits the water 5.22 m in front of the raft. Find the speed of the raft. (Ch 2 #10)
0.74 m/s
Two vectors, A and B, have vector components that are shown (to the same scale) in the drawing. The resultant vector is labeled R. Which drawing shows the correct vector sum of A + B? (1.8)
1
An Australian emu is running due north in a straight line at a speed of 13.0 m/s and slows down to a speed of 10.2 m/s in 4.60 s. (a) What is the magnitude and direction of the bird's acceleration? (b) Assuming that the acceleration remains the same, what is the bird's velocity after an additional 1.00 s has elapsed? (Ch 2 #6)
a) -0.61m/s^2 b) 9.59 m/s
In preparation for this question, review Conceptual Example 7. Vectors A and B satsify the vector equation A + B =0. How does the magnitude and direction of B compare to the magnitude and direction of A? (1.6)
Their magnitudes are the same, but their directions aren't
Physics is the most fundamental of all the sciences. It aims to describe everything in the universe from the very big to the very small. (1.1)
True
Each trigonometric function can be written as the ratio of the lengths of two sides of a right triangle. Do the lengths of the sides of the triangle have to have the same units? (1.4)
Yes
You live in the building on the left in the drawing, and a friend lives in the other building. The two of you are having a discussion about the heights of the buildings, and your friend claims that the height of his building is more than 1.50 times the height of yours. To resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of 21° above the horizontal, whereas your line of sight to the base of the other building makes an angle of 52° below the horizontal. Determine the ratio of the height of the taller building to the height of the shorter building. State whether your friend is right or wrong. (Ch 1 #14)
1.3 (no units), wrong
A fire hose ejects a stream of water at an angle of 31.5 ° above the horizontal. The water leaves the nozzle with a speed of 25.7 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire? (Ch 3 #8)
30m
Two nonzero perpendicular vectors can be added together so their sum is zero. (1.6)
False
Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Swimmer A swims perpendicular to the current and lands on the far shore downstream, because the current has swept him in that direction. Swimmer B swims upstream at an angle to the current and lands on the far shore directly opposite the starting point. Swimmer C swims downstream at an angle to the current in an attempt to take advantage of the current. Who crosses the river in the least time? Note: The width of the river and the velocity of the water with respect to the ground are both constant. (3.4)
Swimmer A
A child is playing on the floor of a recreational vehicle (RV) as it moves along the highway at a constant velocity. He has a toy cannon, which shoots a marble at a fixed angle and speed with respect to the floor. The cannon can be aimed toward the front or rear of the RV. How do the marble's ranges compare from the child's point of view and from the point of view of an observer standing still on the ground? (3.4)
The two ranges are equal from the child's point of view only.
Vectors A, B , C and satisfy the vector equation A + B = C, and their magnitudes are related by the scalar equation A^2 + B^2 =C^2. How is vector A oriented with respect to vector B? (1.6)
The two vectors are perpendicular
A partly-full paint can has 0.418 U.S. gallons of paint left in it. (a) What is the volume of the paint, in cubic meters? (b) If all the remaining paint is used to coat a wall evenly (wall area = 10.8 m2), how thick is the layer of wet paint? Give your answer in meters (Ch 1 #7)
a) 0.0016 m^3 b) 0.000146 m --1 U.S gallon = 3.785 X 10^-3 --(0.418)(3.785 X 10^-3) = 0.0016 or 1.58 X 10^-3 --(1.58 X 10^-3) = 10.8a -- a = 1.46 X 10^-4 or 0.000146
(a) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 4.48 m/s when going down a slope for 3.43 s? (b) How far does the skier travel in this time? (Ch 2 #7)
a) 1.3 m/s^2 b) 7.65 m
An eagle is flying horizontally at 8.7 m/s with a fish in its claws. It accidentally drops the fish. (a) How much time passes before the fish's speed doubles? (b) How much additional time would be required for the speed to double again? (Ch 3 #9)
a) 1.54 s b) 1.9 s
A golf ball rolls off a horizontal cliff with an initial speed of 13.7 m/s. The ball falls a vertical distance of 15.2 m into a lake below. (a) How much time does the ball spend in the air? (b) What is the speed v of the ball just before it strikes the water? (Ch 3 #11)
a) 1.778 s b) 22/15 m.s
A straight track is 1600 m in length. A runner begins at the starting line, runs due east for the full length of the track, turns around and runs halfway back. The time for this run is five minutes. (2.2) a) What is the magnitude of the runner's average velocity? b) What is the runner's average speed?
a) 160 meters per minute b) 480 meters per minute
A space vehicle is coasting at a constant velocity of 18.2 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.395 m/s2 in the +x direction. After 52.6 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction (Ch 3 #7)
a) 27.62 m/s b) 48.74 degrees
The magnitude of a force vector F is 89.2 newtons (N). The x component of this vector is directed along the +x axis and has a magnitude of 78.9 N. The y component points along the +y axis. (a) Find the angle between F and the +x axis. (b) Find the component of F along the +y axis. (Ch 1 #11)
a) 27.8 degrees b) 41.6 N
A jogger travels a route that has two parts. The first is a displacement A of 2.30 km due south, and the second involves a displacement B that points due east. The resultant A + B displacement + has a magnitude of 4.55 km. (a) What is the magnitude of B, and (b) what is the direction of A + B as a positive angle relative to due south? Suppose that A - B had a magnitude of 4.55 km. (c) What then would be the magnitude of B, and (d) what is the direction of A - B relative to due south? (Ch 1 #10)
a) 3.93 km b) 59.66 degrees c) 3.93 km d) 59.66 degrees
A person is standing at the edge of the water and looking out at the ocean (see figure). The height of the person's eyes above the water is h = 1.7 m, and the radius of the Earth is R = 6.38 x 106 m. (a) How far is it to the horizon? In other words, what is the distance d from the person's eyes to the horizon? (Note: At the horizon the angle between the line of sight and the radius of the earth is 90°.) (b) Express this distance in miles (Ch 1 #9)
a) 4657.5 m b) 2.89 mi
One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 1.59 km. They start at the west side of the lake and head due south to begin with. (a) What is the distance they travel? (b) What is the magnitude of the couple's displacement? (c) What is the direction (relative to due east) of the couple's displacement? (Ch 2 #4)
a) 7.49 km b) 2.25 km c) 45 degrees
In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot for 0.0451 s, during which time it experiences an acceleration of 254 m/s2. The ball is launched at an angle of 46.4 ° above the ground. Determine the (a) horizontal and (b) vertical components of the launch velocity. (Ch 3 #3)
a) 7.96 m/s b) 8.36 m/s
Two soccer players start from rest, 38 m apart. They run directly toward each other, both players accelerating. The first player's acceleration has a magnitude of 0.40 m/s2. The second player's acceleration has a magnitude of 0.43 m/s2. (a) How much time passes before the players collide? (b) At the instant they collide, how far has the first player run? (Ch 2 #9)
a) 9.6 s b) 18.43 m