A proton of mass m undergoes a head on collision with a stationary atom of mass 20m. If the initial speed of the proton is 485 m/s, find the speed of the proton after the collision.

Answer 1

momentum conserved:
m*485=Vatom*20m+Vproton*m
so two unknowns, we need another equation. So we use use conservation of energy
1/2 m 485^2=1/2 *20m*Vatom^2 + 1/2 *m*Vpro^2

use the first equation to solve for Vatom in terms of Vproton, put that expression into the second equation (a bit of algebra ensures) and solve for Vproton