# Conservation of linear momentum particle accelerator

## Homework Statement

You are at the controls of a particle accelerator, sending a beam of 3.60×10^7 protons (mass m ) at a gas target of an unknown element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of 3.30×10^7 . Assume that the initial speed of the target nucleus is negligible and the collision is elastic.
a)Find the mass of one nucleus of the unknown element. Express your answer in terms of the proton mass m.
b)What is the speed of the unknown nucleus immediately after such a collision?
This portion I've calculated to be 3.00x10^6.

## Homework Equations

Conservation of linear momentum

## The Attempt at a Solution

I've done research to try and find out how to approach this problem. There's a similar thread from a couple of years ago located here https://www.physicsforums.com/showthread.php?t=145536 that has different values.

I am not entirely sure where to begin, and am having trouble sorting through the suggestions listed in the old thread. I know I'll have to use conservation of linear momentum. My algebra skills are rusty, (public school sucks) so solving for variables is a struggle for me.

From the problem I know Vo (Initial velocity) = 0
And the mass is k (a constant) followed by m.