Chapter 3

A boy throws a rock with an initial velocity of 2.15 m/s at 30.0° above the horizontal. If air resistance is negligible, how long does it take for the rock to reach the maximum height of its trajectory? A) 0.110 s B) 0.194 s C) 0.215 s D) 0.303 s

A

A catapult is tested by Roman legionnaires. They tabulate the results in a papyrus and 2000 years later the archaeological team reads (distances translated into modern units): Range = 0.20 km; angle of launch = π/4; landing height = launch height. What is the initial velocity of launch of the boulders if air resistance is negligible? A) 44 m/s B) 1.4 m/s C) 22 m/s D) 0.69 m/s

A

A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point with no air resistance. What was the angle of launch? A) 69.0° B) 67.4° C) 22.6° D) 44.8°

A

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food? Air resistance is small enough to be ignored. A) He should aim it at the monkey. B) He should aim it below the monkey. C) He should aim it above the monkey.

A

A plane flies directly between two cities, A and 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 65 minless than the trip from A to B. What is the airspeed of the plane, assuming it is the same in both directions? A) 530 mi/h B) 400 mi/h C) 480 mi/h D) 610 mi/h

A

A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s2 directly downward, the stall lasts 5.0 s, and the plane was originally climbing at 25° to the horizontal, what is the velocity after the stall? A) 66 m/s at 17° below the horizontal B) 66 m/s at 17° above the horizontal C) 80 m/s at 37° below the horizontal D) 80 m/s at 37° above the horizontal

A

A plane has an eastward heading at a speed of 156 m/s (relative to the air). A 20.0 m/s wind is blowing southward while 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.

A

A rescue plane flying horizontally at 72.6 m/s spots a survivor in the ocean 182 m directly below and releases an emergency kit with a parachute. Because of the shape of the parachute, it experiences insignificant horizontal air resistance. If the kit descends with a constant vertical acceleration of 5.82 m/s2, how far away from the survivor will it hit the waves? A) 574 m B) 4.54 km C) 406 m D) 602 m

A

A small boat is moving at a velocity of 3.35 m/s when it is accelerated by a river current perpendicular to the initial direction of motion. If the acceleration of the current is 0.750 m/s2, what will be the new velocity of the boat after 33.5 s? A) 25.3 m/s at 82.4° from initial direction of motion B) 25.3 m/s at 7.59° from initial direction of motion C) 640.1 m/s at 82.4° from initial direction of motion D) 640.1 m/s at 7.59° from initial direction of motion

A

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Just as they reach the lake below A) the speed of Alice is larger than that of Tom. B) the splashdown speed of Alice is larger than that of Tom. C) they will both have the same speed. D) the speed of Tom will always be 9.8 m/s larger than that of Alice. E) the speed of Alice will always be 25 m/s larger than that of Tom.

A

An aircraft performs a maneuver called an "aileron roll." During this maneuver, the plane turns like a screw as it maintains a straight flight path, which sets the wings in circular motion. If it takes it 35 s to complete the circle and the wingspan of the plane is 11 m, what is the acceleration of the wing tip? A) 0.18 m/s2 B) 0.99 m/s2 C) 5.6 m/s2 D) 1.0 m/s2

A

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to north to arrive at the destination? A) 4.78° east of north B) 4.76° east of north C) 85.2° west of north D) 4.78° west of north E) 4.76° west of north

A

An electrical motor spins at a constant 2857.0 rev/min. If the armature radius is 2.685 cm, what is the acceleration of the outer edge of the armature? A) 2403 m/s2 B) 844.4 m/s2 C) 241,100 m/s2 D) 84.40 m/s2

A

An electron moves with a constant horizontal velocity of 3.0 × 106 m/s and no initial vertical velocity as it enters a deflector inside a TV tube. The electron strikes the screen after traveling 17.0 cm horizontally and 40.0 cm vertically upward with no horizontal acceleration. What is the constant vertical acceleration provided by the deflector? (The effects of gravity can be ignored.) A) 2.5 × 1014 m/s2 B) 8.3 × 102 m/s2 C) 1.4 × 104 m/s2 D) 1.2 × 1014 m/s2

A

For an object in uniform circular motion, its velocity and acceleration vectors are always perpendicular to each other at every point in the path. A) True B) False

A

If an object travels at a constant speed in a circular path, the acceleration of the object is A) larger in magnitude the smaller the radius of the circle. B) in the same direction as the velocity of the object. C) smaller in magnitude the smaller the radius of the circle. D) in the opposite direction of the velocity of the object. E) zero.

A

If you set the cruise control of your car to a certain speed and take a turn, the speed of the car will remain the same. Is the car accelerating? A) Yes B) No

A

Jan and Len throw identical rocks off a tall building at the same time. The ground near the building is flat. Jan throws her rock straight downward. Len throws his rock downward and outward such that the angle between the initial velocity of the rock and the horizon is 30°. Len throws the rock with a speed twice that of Jan's rock. If air resistance is negligible, which rock hits the ground first? A) They hit at the same time. B) Jan's rock hits first. C) Len's rock hits first. D) It is impossible to know from the information given.

A

Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.5 times that of particle B. The period of particle B is 2.0 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to A) rA/rB = 2.1. B) rA/rB = 4.3. C) rA/rB = 18. D) rA/rB = 0.24. E) rA/rB = 17.

A

What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of 2.78 m/s and air resistance is negligible? A) 0.789 m B) 1.58 m C) 1.39 m D) 0.394 m

A

You want to swim straight across a river that is 76 m wide. You find that you can do this if you swim at an angle ofθ = 28° from the upstream direction at a constant rate of 1.5 m/s relative to the water. At what rate does the river flow? The angle θ is measured from the river bank (directly upstream is θ = 0° while directly across the river is θ = 90°). A) 1.3 m/s B) 0.70 m/s C) 1.6 m/s D) 1.8 m/s

A

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 7.00 revolutions every 10.0 seconds. What is the magnitude of the acceleration of the ball? A) 67.9 m/s2 B) 38.7 m/s2 C) 29.3 m/s2 D) 14.8 m/s2 E) 74.2 m/s2

B

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 over the package. C) be in front of the package. D) depend of the speed of the plane when the package was released.

B

A satellite orbits the earth a distance of 1.50 × 107 m above the planet's surface and takes 8.65 hours for each revolution about the earth. The earth's radius is 6.38 × 106 m. The acceleration of this satellite is closest to A) 0.0690 m/s2. B) 0.870 m/s2. C) 1.91 m/s2. D) 2.72 m/s2. E) 9.80 m/s2.

B

An object has a position given by = [2.0 m + (5.00 m/s)t]î + [3.0 m - (2.00 m/s2)t2]ĵ, where quantities are in SI units. What is the speed of the object at time t = 2.00 s? A) 6.40 m/s B) 9.43 m/s C) 7.00 m/s D) 7.65 m/s E) 13.0 m/s

B

For general projectile motion, when the projectile is at the highest point of its trajectory A) its acceleration is zero. B) its velocity is perpendicular to the acceleration. C) its velocity and acceleration are both zero. D) the horizontal component of its velocity is zero. E) the horizontal and vertical components of its velocity are zero.

B

While an object is in projectile motion (with upward being positive) with no air resistance A) the horizontal component of its velocity remains constant and the horizontal component of its acceleration is equal to -g. B) the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to -g. C) the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to zero. D) the vertical component of both its velocity and its acceleration remain constant. E) the vertical component of its velocity remains constant and the vertical component of its acceleration is equal to -g.

B

A cart is moving with a constant horizontal velocity of 5.00 m/s. A small pebble is launched from the front of the cart with a velocity of 8.00 m/s at 60.0° above the horizontal as measured relative to the cart (see figure) and experiences no significant air resistance. Just as the pebble returns to the level from which it was launched, its distance from the front of the cart is closest to A) 2.83 m. B) 4.60 m. C) 5.66 m. D) 9.19 m. E) 11.3 m.

C

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Compare the time it takes each of them to reach the lake below. A) Alice reaches the surface of the lake first. B) Tom reaches the surface of the lake first. C) Alice and Tom will reach the surface of the lake at the same time.

C

Object A has a position as a function of time given by A(t) = (3.00 m/s)tî + (1.00 m/s2)t2ĵ. Object B has a position as a function of time given by B(t) = (4.00 m/s)tî + (-1.00 m/s2)t2ĵ. All quantities are SI units. What is the distance between object A and object B at time t = 3.00 s? A) 34.6 m B) 15.0 m C) 18.3 m D) 3.46 m E) 29.8 m

C

A hockey puck slides off the edge of a table with an initial velocity of 28.0 m/s. and experiences no air resistance. The height of the tabletop 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°

D

An object has a position given by r = [2.0 m + (3.00 m/s)t]î + [3.0 m - (2.00 m/s2)t2]ĵ, where all quantities are in SI units. What is the magnitude of the acceleration of the object at time t = 2.00 s? A) 1.00 m/s2 B) 0.00 m/s2 C) 0.522 m/s2 D) 4.00 m/s2 E) 2.00 m/s2

D

An object moves in a circle of radius R at constant speed with a period T. If you want to change only the period in order to cut the object's acceleration in half, the new period should be A) T/4. B) T/2. C) T/sqrt2 . D) T sqrt2. E) 4T.

D

A ball is thrown at a 60.0° angle above the horizontal across level ground. It is thrown from a height of 2.00 m above the ground with a speed of 20.0 m/s and experiences no appreciable air resistance. The time the ball remains in the air before striking the ground is closest to A) 16.2 s. B) 3.07 s. C) 3.32 s. D) 3.53 s. E) 3.64 s.

E

A long-distance swimmer is able to swim through still water at 4.0 km/h. She wishes to try to swim from Port Angeles, Washington, directly north to Victoria, British Columbia, a distance of 50 km. An ocean current flows through the Strait of Juan de Fuca from west to east at 3.0 km/h. In what direction (relative to north) should she swim to make the crossing along a straight line between the two cities? A) 37° west of north B) 37° east of north C) 41° west of north D) 41° east of north E) 49° west of north

E

A rock is thrown at a window that is located 18.0 m above the ground. The rock is thrown at an angle of 40.0° above horizontal. The rock is thrown from a height of 2.00 m above the ground with a speed of 30.0 m/s and experiences no appreciable air resistance. If the rock strikes the window on its upward trajectory, from what horizontal distance from the window was it released? A) 53.2 m B) 48.7 m C) 71.6 m D) 29.8 m E) 27.3 m

E