 #1
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 1
 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 ?
(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 ?