## Questions

A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second. The boy throws a ball vertically upward with a velocity of 10 meters per second relative to the elevator. What is the velocity of the ball, MAGNITUDE AND DIRECTION, relative to the elevator shaft the instant the boy releases the ball?

### Answer

**The final answer to this question is 20 meters per second downward.**

### Explanation

The elevator is travelling downward with a velocity of 30 meters per second (30 m/s)

Additionally, the boy throws the ball vertically upward with a velocity of 10 meters per second relative to the elevator.

We can now clearly see that the elevator is moving down when the boy decides to throw the ball upward. Due to gravitational force, the ball will reach a maximum height and then start coming back to the elevator.

The two velocities are moving in opposite direction. However, the upward velocity must return back to the downward velocity due the force of gravity.

For us to find the total velocity, magnitude and direction of the ball. We need to subtract the upward velocity of the ball from the downward velocity of the elevator.

Hence,

Total velocity, magnitude and direction, v_{T} = 30 + (-10) = 20 m/s downward

**Therefore, the total velocity, magnitude and direction, v _{T} of the ball is 20 meters per second down.**

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