Homework Help: Kinetic and Potential Energy

1. Oct 18, 2003

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

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?

2. Oct 19, 2003

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"!