Question

A proton, moving with a velocity of vinitial i, collides elastically with another proton that is initially at rest. Assuming that the 2 protons have equal speeds after the collision, find (a) the speed of each proton after the collision in terms of vinitial and (b) the direction of the velocity vectors after the collision.

I found part (a) to be Vfinal= Vinitial(sqroott/2)

Answer 1

The keyword here is "elastically".
This means that
1. if they move with the same velocity after impact, they cannot move in the same direction.
2. Energy is conserved, so that
mv0²=mv1²+mv1²
from which you can conclude v1=v0/√2.