# Question regarding velocity

1. Jul 18, 2014

### fightboy

A device launches a ball straight up from the edge of a cliff so that the ball falls and hits the ground at the base of the cliff. The device is then turned so that a second, identical ball is launched straight down from the same height. Assuming the initial speed of the ball is the same in both cases, does the second ball hit the ground with a velocity that is higher than, lower than, or the same as the first ball? Explain your answer.

Initially i thought the answer was that the second ball hits the ground with a higher velocity, but the answer ended up being that the velocities would be identical. I don't quite understand this concept, because it seems as though the one being launched directly down would achieve a higher velocity due to having a stronger downward acceleration.
Is there anyone who could explain this concept to a physics noob like me in an easy, uncomplicated way? Thanks!

2. Jul 18, 2014

### Nathanael

When the ball is launched up, gravity is accelerating (reducing the speed of) the ball.

The ball reaches a maximum height.

The speed of the ball at this max height is zero, then the ball starts to fall.

The reason it falls, of course, is because gravity is accelerating it (now increasing the speed of it).

The amount that it is accelerated on the way up is the same amount that it is accelerated on the way down.

This means that once it has fallen (from maximum height) back to the launch height, (at the top of the cliff) it will have the same speed as it was launched with, but now it will be in the downward direction.

In summary, the reason is simply that the ball is accelerated by the same amount on the way up as it is on the way down.
(So the change in speed on the way up is the same as the change in speed on the way down.)

3. Jul 19, 2014

### CWatters

What N said.

If you fire something up in the air it always hits the ground at the same velocity (ignoring air resistance). This is due to conservation of energy.. The initial KE is converted to PE on the way up and back to KE on the way down.

So in this problem the first ball fired vertically upwards at Vi passes the gun on the way back down also at Vi. From there on both shots are the same.