Kinetic and Potential Energy

[Aerospace]

A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential energy of 50 Joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 Joules. Air friction is negligible. The maximum height 'h' reached by the ball is most nearly
1. h = 30 m
2. h = 50 m
3. h = 10 m
4. h = 20 m
5. h = 40 m
(all answers are approximate)

haha, I think I finally figured it out, but let me make sure if I'm right. I'm thinking that since both the Potential Energy and Kinetic energy are equal, that means that the ball is half way through it's path, right? So that should mean that the height is 20 meters.

Am I correct?

 

[HallsofIvy]

A little more precise way of saying this (as opposed to "yep"!)
is that you are given that the total energy is 100 Joules. The ball will be at its highest point when its speed is 0 so all the energy is converted to potential energy: mgh= 100. Since the potential energy at 10 meters above the ground was 50, you know that mg(10)= 50 or that mg= 5. Thus mgh= = 5h= 100 so h= 20.

Or- since the kinetic energy and potential energy are the same, when there is no kinetic energy the potential energy will be twice as great. Twice the potential energy, twice the height!

Or- in the succinct words of enigma: "Yep"!

 

[M98Ranger]

Yes, you are correct! Since the potential energy and kinetic energy are equal at a height of 10 meters, that means the ball is halfway through its path and will reach a maximum height of 20 meters. This is because as the ball is thrown upward, it gains potential energy and loses kinetic energy due to gravity. At the highest point, all of the kinetic energy is converted into potential energy. So, the maximum height reached by the ball is 20 meters.