# More quick work and energy questions

An object hits a wall and bounces back with half if its original speed. What is the ratio of the final kinetic energy to the initial kinetic energy?
I am not sure I understand the question, is it 1:2?

A ball drops some distance and gains 30 J of kinetic energy. Do not ignore air resistance. How much gravitational potential did the ball lose?
I would say more than 30J since we have to take air resistance into consideration.

Thanks!

## Answers and Replies

radou
Homework Helper
An object hits a wall and bounces back with half if its original speed. What is the ratio of the final kinetic energy to the initial kinetic energy?
I am not sure I understand the question, is it 1:2?

Not so fast. Write down the kinetic energies and look at the ratio.

First is 1 and second is 0.5 => 1/0.5 =2. Is this correct?

radou
Homework Helper
First is 1 and second is 0.5 => 1/0.5 =2. Is this correct?

No, it isn't. The first kinetic energy is 1/2 m v^2, and the second is 1/2 m (1/2 v)^2. What is their ratio?

AlephZero
Science Advisor
Homework Helper
First is 1 and second is 0.5 => 1/0.5 =2. Is this correct?

No - the kinetic energy of the object is (1/2)mv^2.

I am not sure I get it, but it looks like 1:0.5 to me...

radou
Homework Helper
I am not sure I get it, but it looks like 1:0.5 to me...

Do you know how to take the ratio of 1/2 m (1/2 v)^2 (final kinetic energy) and 1/2 m v^2 (initial kinetic energy)?

I guess not... It's ok, I'll figure it out.

Thanks!