Air Resistance and Terminal Velocity

[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 realize 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,

 

[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.

 

[Hazeel]

Ah ok, that helps a lot. Thank you!

 

[Hazeel]

Can anyone else provide any other information please?

 

[radou]

Can anyone else provide any other information please?

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.

There is no other information, you got the answer to your question in the posts above. If you meant something else, maybe you should rebuild your question.

 

[OlderDan]

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 realize 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,

I'm not sure what topic you are studying, but it may be that this is a question about air resistance, not energy conservation. Skydivers achieve a terminal velocity when the force of air resistance becomes equal to their weight. Air resistance will vary with height as well as speed. Where do you think the resistance will be greatest? Why?