Class Practice
14. A slower-moving car is traveling behind a faster-moving bus. The velocities of the two vehicles are as follows:
v CG 5 velocity of the Car relative to the Ground = 112 m/s
v BG 5 velocity of the Bus relative to the Ground = 116 m/s
A passenger on the bus gets up and walks toward the front of the bus with a velocity of v PB , where v PB 5 velocity of the
Passenger relative to the Bus = 12 m/s. What is v PC , the velocity of the Passenger relative to the Car?
(a) 12 m/s 16 m/s 12 m/s 130 m/s
(b) 22 m/s 16 m/s 12 m/s 126 m/s
(c) 12 m/s 16 m/s 12 m/s 16 m/s
(d) 22 m/s 16 m/s 12 m/s 12 m/s
15. Your car is traveling behind a jeep. Both are moving at the same speed, so the velocity of the jeep relative to you
is zero. A spare tire is strapped to the back of the jeep. Suddenly the strap breaks, and the tire falls off the jeep. Will
your car hit the spare tire before the tire hits the road? Assume that air resistance is absent. (a) Yes. As long as the car
doesn’t slow down, it will hit the tire. (b) No. The car will not hit the tire before the tire hits the ground, no matter
how close you are to the jeep. (c) If the tire falls from a great enough height, the car will hit the tire. (d) If the car is
far enough behind the jeep, the car will not hit the tire.
16. The drawing shows two cars traveling in different directions with different speeds. Their velocities are:
v AG = velocity of car A relative to the Ground = 27.0 m/s, due east
v BG = velocity of car B relative to the Ground = 21.0 m/s, due north
The passenger 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 passenger of car B? In other words, what is the velocity v AB of car A relative to car B? Give
the directional angle of v AB with respect to due east. (34.2 m/s, 37.9 SE)
SECTION 3.4 RELATIVE VELOCITY
52. Two cars, A and B, are traveling in the same direction, although car A is 186 m behind car B. The speed of
A is 24.4 m/s, and the speed of B is 18.6 m/s. How much time does it take for A to catch B? (32.1s)
53. ssm A swimmer, capable of swimming at a speed of 1.4 m/s in still water (i.e., the swimmer can swim with
a speed of 1.4 m/s relative to the water), starts to swim directly across a 2.8-km-wide river. However, the current is
0.91 m/s, and it carries the swimmer downstream. (a) How long does it take the swimmer to cross the river?
(2.0103 s) (b) How far downstream will the swimmer be upon reaching the other side of the river? (1.8103 m)
54. Two friends, Barbara and Neil, are out rollerblading. With respect to the ground, Barbara is skating due
south at a speed of 4.0 m/s. Neil is in front of her. With respect to the ground, Neil is skating due west at a speed of
3.2 m/s. Find Neil’s velocity (magnitude and direction relative to due west), as seen by Barbara. (5.1 m/s @ 51
NW)
55. The escalator that leads down into a subway station has a length of 30.0 m and a speed of 1.8 m/s relative to
the ground. A student is coming out of the station by running in the wrong direction on this escalator. The local
record time for this trick is 11 s. Relative to the escalator, what speed must the student exceed in order to beat the
record? (4.5 m/s)
56. A police officer is driving due north at a constant speed of 29 m/s relative to the ground when she notices a
truck on an east–west highway ahead of her, driving west at high speed. She finds that the truck’s speed relative to
her car is 48 m/s (about 110 mph). (a) Sketch the vector triangle that shows how the truck’s velocity relative to the
ground is related to the police car’s velocity relative to the ground and to the truck’s velocity relative to the police
car. The sketch need not be to scale, but the velocity vectors should be oriented correctly and bear the appropriate
labels. (b) What is the truck’s speed, relative to the ground? (38 m/s)
59. You are in a hot-air balloon that, relative to the ground, has a velocity of 6.0 m/s in a direction due east. You
see a hawk moving directly away from the balloon in a direction due north. The speed of the hawk relative to you
is 2.0 m/s. What are the magnitude and direction of the hawk’s velocity relative to the ground? Express the
directional angle relative to due east. (6.3 m/s, 18 NE)
60. The captain of a plane wishes to proceed due west. The cruising speed of the plane is 245 m/s relative to the
air. A weather report indicates that a 38.0-m/s wind is blowing from the south to the north. In what direction,
measured with respect to due west, should the pilot head the plane? (8.92 SW)
Homework 1
* 61. A person looking out the window of a stationary train
notices that raindrops are falling vertically down at a speed of
5.0 m/s relative to the ground. When the train moves at a
constant velocity, the raindrops make an angle of 25° when
they move past the window, as the drawing shows. How fast
is the train moving? (2.3 m/s)
* 62. Relative to the ground, a car has a velocity of 16.0 m/s, directed due north. Relative to this car, a truck has a
velocity of 24.0 m/s, directed 52.0° north of east. What is the magnitude of the truck’s velocity relative to the
ground? (37.9 m/s)
* 63. ssm Mario, a hockey player, is skating due south at a speed of 7.0 m/s relative to the ice. A teammate
passes the puck to him. The puck has a speed of 11.0 m/s and is moving in a direction of 22° west of south, relative
to the ice. What are the magnitude and direction (relative to due south) of the puck’s velocity, as observed by
Mario? (5.2 m/s @ 52 WS)