Can Two Protons Have the Same Speed After an Elastic Collision?

[Mustard]

Homework Statement

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

Relevant Equations

Equations for first problem:
m1v1i + m2v2i = (m1+m2)vf
v1i + v1f = v2i + v2f
and we know v1f = v2f
m2v2i = 0 since 2nd proton is initially at rest
mass of proton = (1.67 × 10^-27) kg

m1v1i + m2v2i = (m1+m2)vf
(1.67 × 10^-27)v1i = (1.67 × 10^-27 + 1.67 × 10^-27) vf
(1.67 × 10^-27/3.34 × 10^-27)v1i = (3.34 × 10^-27/3.34 × 10^-27) vf
(1.67 × 10^-27/3.34 × 10^-27)v1i = vf
(0.5)(v1i) = vf

not sure what to do from here nor if I'm in the correct path ?

 

[etotheipi]

Hmm. About the question: an elastic collision between equal masses where one is initially at rest at the start will result in the other one coming to rest, and the one that was at initially rest moving off at the same speed. Is it possible for both to have the same speed after the collision? I don't think so...