# Elastic Collision: Two carts

1. Dec 1, 2014

### ngu9997

1. The problem statement, all variables and given/known data
Cart 1 on ball-bearing wheels is moving at 4m/sec. It rolls down the hill and hits a stationary cart 2. The collision is elastic. The height of the hill is 1.02 m. Mass of Cart 1: 200 grams; Mass of Cart 2: 400 grams: Find the velocity of cart 1 at point B.

2. Relevant equations
m1v1+m2v2=m1v1'+m2v2'; this is all I can think of but I don't have velocity 1 or 2 prime and I'm not sure how to find either of them. I was wondering if I had to use one of the basic kinematic equations because the height of the hill was given, but I'm not sure.

3. The attempt at a solution
I have the correct answer (6m/s) , but I would like to know how to do it and I've looked at a couple of kinematic equations with distance in them, but nothing I try seems to work.

2. Dec 1, 2014

### Orodruin

Staff Emeritus
Please provide us with your attempted solution, it is not enough to simply say you know what the answer is.

3. Dec 1, 2014

### ngu9997

For my attempt at finding the solution to this problem I tried to use the equation: vf^2=vi^2+2ad thinking that acceleration played a part in the cart's velocity. When I plugged in all the numbers to the variables I received a negative radical of sqrt: -3.992 which clearly wasn't the answer. After receiving this answer I looked at the picture of the diagram (which I am unable to provide) more clearly and after cart 1 moves down the hill it travels a little more before colliding with cart 2 and the distance is not told. I am unable to think an equation that would work.

4. Dec 1, 2014

### ngu9997

Sorry, acceleration of gravity*

5. Dec 1, 2014

### Orodruin

Staff Emeritus
What conservation laws do you know of? Which could be applicable here?

6. Dec 1, 2014

### ngu9997

I know of the law of momentum conservation and the equation m1v1+m2v2=m1v1'+m2v2' describes this principle, and I have a good feeling that this equation would have to be used but I don't have velocity 2 prime so I can't find velocity 1 prime.

7. Dec 1, 2014

### Orodruin

Staff Emeritus
Could you perhaps relate them with another conservation law?