# Forces/Effect Question

1. Oct 16, 2006

### Hazeel

We have been given an assignment with the question:

"How does the height of a body falling through the air effect its velocity?"

It's clear that as the height the object is dropped from, the greater the velocity of the object will be. However, I was wondering if anybody could give me any help with some equations/maths that proves this. I realise this is simple stuff, however I can't quite get my head around the thought and think of the equation that would be used.

I would appreciate any equation based help to be of a relatively simple nature as my Physics is not very advanced.

Also, any help with how the below equation can help to prove that height will increase the velocity of a falling object would be appreciated to.

V2 = 2gh

V2 being V squared.

Thank you,

2. Oct 16, 2006

### Repetit

The equation you wrote comes from:

$$\frac{1}{2}m v^2 = m g h$$

This equation represents the fact that potential energy (right hand side) is converted to kinetic energy (left hand side) on falling a distance h through the gravitational field. Cancelling m on both sides and multiplying by 2 gives what you wrote:

$$v^2 = 2 g h$$

Which expresses the change in speed when falling a distance h.

3. Oct 16, 2006

### Hazeel

Ah ok, that helps a lot. Thank you!

4. Oct 18, 2006

### Hazeel

Can anyone else provide any other information please?

5. Oct 18, 2006

Maybe it could be stated a bit more precisely - $$v^2 = 2gh$$ represents the speed the object has just before it touches the ground, and that very speed depends on the height h from which the object is dropped.