You are on a rooftop and you throw one ball straight down and another straight up. The second ball, after rising, falls and also strikes the ground below.

If air resistance can be neglected and if your downward and upward initial speeds are the same, how will the speed of the balls compare upon striking the ground?

1. The speed of the second ball is smaller than that of the first one.

2. The speed of the second ball is larger than that of the first one.

3. They have same speed.

4. More information is needed

Answer: 3. They have same speed

Explanation:

When you throw the second ball straight up from the top of the roof at a particular velocity. The velocity at which it will reach it maximum height is zero, but the velocity at which it will fall down to the same level you threw it up (roof top) will be equal to the same velocity at which you initially threw it up but different direction, neglecting air resistance. And since it will come down to the roof top at that same velocity which is also the same as the velocity on the first ball, they will both reach the ground at the same speed.

Also, looking at it from the energy aspect

They both left the top of the building with the same kinetic energy (they were thrown at the same speed but different direction) so they will both end up with the same energy when they reach the ground.

Assuming their initial Velocity is v

First ball - at the roof top starts with velocity v downward

Second ball starts with velocity v upward and comes down with the same velocity v downward at the roof top

Since they will both possess the same speed at the roof top they will both touch the ground with the same velocity but at different time.