# Relativistic kinetic energy and momentum

1. Jan 28, 2017

### Cocoleia

1. The problem statement, all variables and given/known data
A proton has a speed of 0.2c. Find the speed of an electron that has (a) the same kinetic energy as the proton, and (b) the same momentum as the proton.

2. Relevant equations
K=ϒmc^2-mc^2

3. The attempt at a solution

This is what I did for the same kinetic energy part, but I would end up with a negative under my square root. I found the formula in my notes, I'm not really sure what to do but I tried something. Can anyone offer me some guidance? I have not attempted the momentum part yet

2. Jan 28, 2017

### TSny

You are OK all the way up to your final expression for v. You made a minor mistake in solving for v. Check your work to see if you can find the mistake.

Also, you can rearrange $\frac{1}{\frac{K+mc^2}{mc^2}}$ to a simpler fraction.

3. Jan 28, 2017

### Cocoleia

It will be multiplied by a negative c ?

4. Jan 28, 2017

### TSny

Sorry, but I'm not sure what you are saying here.

5. Jan 28, 2017

### Cocoleia

My mistake was that when I solved for v I forgot the negative sign

6. Jan 28, 2017

### TSny

Yes. Good.

7. Jan 28, 2017

### Cocoleia

This is what I did for when they have the same momentum

It just seems weird that it gives me the speed of light I feel like that's probably wrong.

8. Jan 28, 2017

### TSny

Looks good, but if your calculator is accurate enough, you should find that the answer for v is slightly less than c.

9. Jan 28, 2017

### Cocoleia

Ok, it was a bit less but I rounded it. I could right the exact answer