elastic collision question?

Question

Two particles, of masses m and 3m, are moving toward each other along the x-axis with the same initial speeds of 7.27 m/s. Mass m is travelling to the left, and mass 3m is traveling to the right. They undergo a head-on elastic collision and each rebounds along the same line as it approached.

Find the final speed of the heavier particle. answer in m/s

i have no idea what to do.

Answer 1

The conservation of momentum can be written as
m1u1-m2u2=-m1v1+m2v2

Assuming that the kinetic energy was also conserved

.5m1u1^2 + .5m2u2^2= 0.5m1v1^2 + 0.5m2v2^2
m1u1^2 + m2u2^2= m1v1^2 + m2v2^2
since u1=u2
(7.27 )^2 [m+3m]=mv1^2 + 3mv2^2

211 =[v1^2 + 3v2^2]
v1= sqrt(211-3v2^2)
substitute v1 in to the momentum equation and solve for v2.