find all the unknowns in the problem.?

Question

An alpha particle, m=4 (in atomic units), collides elastically with a calcium atom, M=20, at rest. The initial velocity of the alpha particle is Vî m/s. After collision the alpha particle has a velocity of 10î - 5j m/s. If the velocity of the calcium atom after collision is Vx î + Vyj find all the unknowns in the problem.

Answer 1

The momentum is conceived

(m1)Vi=m1(10î - 5j )+m2(Vxi+Vyj)
m1 - alpha particle
m2 - sodium atom

grouping into x and y componeents we have

V=10 m1 + Vx m2
0=-5 m1 + Vy m2

Vy=5m1/m2= 5(4)/20=1m/s
Vx=(V-10 m1)/m2