Physics: Relative Motion and Reference Frames Worksheet

Question 1

A student stands on a sidewalk and watches a bus travel east at 12 m/s. A passenger on the bus walks toward the front of the bus, also east, at 1.5 m/s relative to the bus. What is the passenger's velocity relative to the sidewalk?

Accepted Answer

The passenger's velocity relative to the sidewalk is 13.5 m/s east. The walking velocity relative to the bus adds to the bus velocity because both are in the same direction.

Question 2

A train moves north at 25 m/s relative to the ground. A person on the train walks south at 2 m/s relative to the train. What is the person's velocity relative to the ground?

Accepted Answer

The person's velocity relative to the ground is 23 m/s north. The walking motion is opposite the train's motion, so 2 m/s is subtracted from 25 m/s.

Question 3

Two cars travel on a straight highway. Car A moves east at 30 m/s, and Car B moves east at 22 m/s. What is the velocity of Car A relative to Car B?

Accepted Answer

The velocity of Car A relative to Car B is 8 m/s east. Car A is moving 8 m/s faster than Car B in the same direction.

Question 4

Two runners move toward each other on a straight track. Runner A moves east at 6 m/s, and Runner B moves west at 5 m/s. What is Runner A's velocity relative to Runner B?

Accepted Answer

Runner A's velocity relative to Runner B is 11 m/s east. If east is positive, Runner A has velocity +6 m/s and Runner B has velocity -5 m/s, so 6 - (-5) = 11 m/s.

Question 5

A boat travels east across a river at 4 m/s relative to the water. The river current flows east at 1.5 m/s relative to the shore. What is the boat's velocity relative to the shore?

Accepted Answer

The boat's velocity relative to the shore is 5.5 m/s east. The boat's velocity relative to the water and the water's velocity relative to the shore are in the same direction, so they add.

Question 6

A boat points straight north and moves at 3 m/s relative to the water. The river current moves east at 4 m/s relative to the shore. What is the boat's speed relative to the shore?

Accepted Answer

The boat's speed relative to the shore is 5 m/s. The north and east velocity components are perpendicular, so the speed is found using the Pythagorean theorem: square root of 3 squared plus 4 squared equals 5.

Question 7

A plane flies north at 80 m/s relative to the air. A wind blows south at 15 m/s relative to the ground. What is the plane's velocity relative to the ground?

Accepted Answer

The plane's velocity relative to the ground is 65 m/s north. The wind is opposite the plane's motion, so the ground velocity is 80 m/s minus 15 m/s.

Question 8

A plane flies east at 120 m/s relative to the air. A wind blows north at 50 m/s relative to the ground. What is the plane's speed relative to the ground? Round to the nearest meter per second.

Accepted Answer

The plane's speed relative to the ground is about 130 m/s. The east and north components are perpendicular, so the speed is the square root of 120 squared plus 50 squared, which equals 130 m/s.

Question 9

A skateboarder rides west at 7 m/s relative to the ground. A friend jogs west at 3 m/s relative to the ground. From the friend's reference frame, what is the skateboarder's velocity?

Accepted Answer

From the friend's reference frame, the skateboarder's velocity is 4 m/s west. The skateboarder is moving west 4 m/s faster than the friend.

Question 10

A ball is thrown straight up inside a train moving at constant velocity. Ignore air resistance. Describe the ball's motion as seen by a passenger on the train and as seen by an observer standing beside the tracks.

Accepted Answer

A passenger on the train sees the ball move straight up and straight down. An observer beside the tracks sees the ball follow a curved path because the ball keeps the train's horizontal velocity while also moving vertically.

Question 11

A cyclist moves east at 10 m/s relative to the ground. A car moves west at 20 m/s relative to the ground. If east is positive, what is the velocity of the cyclist relative to the car?

Accepted Answer

The velocity of the cyclist relative to the car is 30 m/s east. Using east as positive, the cyclist's velocity is +10 m/s and the car's velocity is -20 m/s, so 10 - (-20) = 30 m/s.

Question 12

A moving walkway in an airport carries people east at 1.2 m/s relative to the floor. A traveler walks west on the walkway at 0.8 m/s relative to the walkway. What is the traveler's velocity relative to the floor?

Accepted Answer

The traveler's velocity relative to the floor is 0.4 m/s east. The walkway moves east faster than the traveler walks west, so the net motion relative to the floor is east at 1.2 - 0.8 = 0.4 m/s.

Physics: Relative Motion and Reference Frames

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