Practice Relative Velocity in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Relative velocity is the velocity of one object as measured from the reference frame of another object.

How fast something seems to move depends on who is watching.

Showing a random 20 of 50 problems.

Example 1

medium
Train A at 25 m/s25\text{ m/s} east passes train B at 15 m/s15\text{ m/s} east on a parallel track. Velocity of B in A's frame?

Example 2

medium
Is relative velocity a scalar or a vector quantity?

Example 3

medium
A swimmer swims 2 m/s2\text{ m/s} relative to water across a current of 1.5 m/s1.5\text{ m/s} at right angles. Find swimmer's ground speed.

Example 4

easy
Two cars approach head-on: A at 3030 m/s east, B at 2020 m/s west. Find their closing speed.

Example 5

challenge
In still air a plane flies 250250 m/s. It must fly due north while a 7070 m/s east wind blows. Find its ground speed due north (round to nearest m/s).

Example 6

medium
A plane has airspeed 200 m/s200\text{ m/s} east. A 50 m/s50\text{ m/s} wind blows from north to south. Find ground velocity (magnitude and direction).

Example 7

medium
A jet flies 200200 m/s east into a 3030 m/s east headwind... actually the wind blows west at 3030 m/s. Find the ground speed.

Example 8

easy
Car A moves 2020 m/s east, car B moves 1212 m/s east. Find A's velocity relative to B.

Example 9

easy
Two runners side by side at 44 m/s. Velocity of one relative to the other?

Example 10

challenge
From a car moving 25 m/s25\text{ m/s} east, a passenger throws a ball 15 m/s15\text{ m/s} east relative to the car. A pedestrian on the ground observes the ball. Find the ball's ground velocity. If the car then decelerates at 2 m/s22\text{ m/s}^2, does the ball's ground velocity change after release?

Example 11

medium
A swimmer moves 1.5 m/s1.5\text{ m/s} relative to water; the river current is 2.0 m/s2.0\text{ m/s}. Swimmer heads directly across (perpendicular to current). Find ground speed.

Example 12

hard
A boat must cross a 100 m100\text{ m}-wide river to a point directly opposite. Boat speed relative to water is 5 m/s5\text{ m/s}; current is 3 m/s3\text{ m/s}. At what angle upstream must the bow point, and what is the crossing time?

Example 13

easy
Two cars approach head-on: A at 25 m/s25\text{ m/s} east, B at 15 m/s15\text{ m/s} west. Find their closing speed.

Example 14

challenge
Two trains 10001000 m apart approach: A at 3030 m/s, B at 2020 m/s (toward each other). When do they meet?

Example 15

easy
A boat moves 4 m/s4\text{ m/s} east relative to water; water moves 3 m/s3\text{ m/s} west. Find the boat's speed relative to ground.

Example 16

easy
Why must direction be tracked when combining velocities?

Example 17

medium
Two cars approach head-on: A at 18 m/s18\text{ m/s} east, B at 12 m/s12\text{ m/s} west, initially 300 m300\text{ m} apart. When do they meet?

Example 18

medium
Person walks 22 m/s forward on a train going 1818 m/s; another walks 22 m/s backward. Find each person's ground velocity.

Example 19

hard
Two cyclists ride toward each other, each at 4 m/s4\text{ m/s}, initially 200 m200\text{ m} apart. A bee flies 8 m/s8\text{ m/s} between them until they meet. Find total bee distance.

Example 20

easy
A walkway moves 1.2 m/s1.2\text{ m/s} east. A person walks 0.8 m/s0.8\text{ m/s} east on it. Speed relative to ground?