# Speed in relation to angles

1. Jan 14, 2009

### nvez

[RESOLVED] Speed in relation to angles

1. The problem statement, all variables and given/known data
You leave a ball roll down 3 different inclined plans with the same height. They each have 30, 45 & 60 degrees of incline respectively. Compare the sped of each of these plans

Height = constant, doesn't change
Angles of plans = 30, 45, 60

2. Relevant equations
None that I know of.

3. The attempt at a solution
I honestly do not see a way how to resolve this problem, if anyone can just shed any light, I know we're working in energy at the moment but I cannot find a way to get information with just an angle.

Last edited: Jan 14, 2009
2. Jan 14, 2009

### LowlyPion

That would be correct. Potential energy at the top will be kinetic energy at the bottom.

They will take different times to reach the bottom ... but at the bottom they will be going at the same speed. (Assuming there is no slipping at the steeper angle or bouncing on impact at the bottom etc.)

3. Jan 14, 2009

### nvez

I _think_ I got it, this is what I did

$$mgh = 1/2mv^{2}$$

m = m therefore removed.

$$gh = 1/2v^{2}$$

take 1/2 on other side becomes 2

$$2gh = v^{2}$$

take the ^2 and make it sqrt the other side

$$\sqrt{2gh} = v$$

Therefore we conclude that the only variables that matter in it's speed is the gravity and height, which is the same in all 3 problems therefore it will arrive at the same speed because gravity and height are constant?

Thanks in advanced if I'm correct. :)

4. Jan 14, 2009

### LowlyPion

That's correct.

5. Jan 14, 2009

### nvez

Thank you very much again, I really appreciate it! :)