# Worksheet: Relative Motion

In this worksheet, we will practice defining the positions, displacements, and velocities of objects compared with those of other objects.

Q1:

The points a, b, c, d, and e are shown in the diagram. How far north of a is c?

How far west of a is b?

How far south of a is e?

How far east of a is d?

How far north of e is c?

How far south of e is d?

How far east of d is b?

How far west of b is c?

Q2:

An airplane flying horizontally in a straight line moves parallel to the ground at a speed of 450 m/s. A second airplane flies below, in the opposite horizontal direction, moving parallel to the ground at a speed of 100 m/s. Which of the diagrams (a), (b), (c), and (d) correctly shows how the velocities of the airplanes can be combined to find the speed at which the airplanes move relative to each other? • A(d)
• B(c)
• C(a)
• D(b)

Q3:

Three walkers stand at the positions , , and shown in the diagram. The walkers all have heights of 1.75 m. The walker at position picks up a stone from the ground and throws it vertically upward to a maximum height that is 7.25 m above her head. How far above the head of the walker at position is the stone when it is at its maximum height?

How far below the feet of the walker at position is the stone when it is at its maximum height?

Q4:

Snowflakes in a snowstorm fall vertically downward at 0.12 m/s. The snowflakes fall in the air around a 1.6 m tall traveler who walks across the snowy ground at 0.72 m/s. The snowflakes are blown eastward at 0.36 m/s by the wind. Consider snowflakes to be initially located directly above the traveler’s head and at the height above the ground of the top of the traveler’s head.

The traveler walks westward. What distance east of the traveler does a snowflake land?

The traveler walks eastward. What displacement east of the traveler does a snowflake land?

Q5:

Cars A and B drive in opposite directions to each other, A at 20 m/s and B at 15 m/s, parallel to the sides of a road, as shown in the diagram. What is the rate of the decrease of the length , the distance between the cars in the direction parallel to the road? Q6:

A rocket is launched from Earth at point , as shown in the diagram. The rotation of Earth results in the rocket having a velocity parallel to Earth’s surface at , shown by the straight red arrow in the diagram. This velocity is 460 m/s. Earth moves through space at 30 km/s, the Moon’s orbital speed around Earth is 1,020 m/s, and the speed at which the rocket moves perpendicular to Earth’s surface is 830 m/s. An observer on the Moon at point watches the rocket through a telescope at the moment that points and are aligned perpendicular to the velocity of the Moon. What is the relative speed of the rocket and the observer perpendicular to the observer?

What is the relative speed of the rocket and the observer along the line between and ?

Q7:

Cars A and B drive in the same direction, A at 10 m/s and B at 25 m/s, parallel to the sides of a road, as shown in the diagram. What is the rate of the increase of the length d, the distance between the cars in the direction parallel to the sides of the road? Q8:

A train moves along tracks at 32 m/s. On the train are passengers A and B. Passenger A walks along the train car at 2 m/s, in the opposite direction to the train’s motion, as shown in the diagram. Passenger B stands in the train car and moves at the same speed as the car. Person C is outside the train, walking in the same direction as the train, moving past the train tracks at 1 m/s. At what speed does passenger A move toward passenger B?

At what speed does passenger A move past the train tracks?

At what horizontal speed does passenger B move away from person C?

At what horizontal speed does passenger A move away from person C?