Momentum with particles

[shotgunbob]

1. The problem statement, all variables and given/known data
You are at the controls of a particle accelerator, sending a beam of (1.5x10^7) m/s (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 1.2 x 10^7 m/s. Assume the initial speed of the target nucleus is negligible and that the collision is elastic.

a) Find the mass of one nucleus of the unknown element.
b) What is the speed of the unknown nucleus immediately after such a collision.


2. Relevant equations
p=mv
1/2mv^2 = KE
Elastic collisions= momentum and KE conserved


3. The attempt at a solution
(m)(1.5x10^7) + Nucleus (0 v)=(m)(1.2x10^7)+ (nucleus)(v?) = Pre and Post momentum of particle

I set the equations against each other but I just cant figure it out
Thanks in advance!

[Kurdt]

You know that the beam is composed of protons. You can look up the mass of a proton in a table. What you have here since the collision is elastic, is a system of two equations with two unknowns. One will be a conservation of momentum equation and the other a conservation of kinetic energy.