Two unknowns require two equations for this situation of moving particles. You need a momentum relation and the kinetic energy relation for the particles: Before = After
1/2 m1v1
2 + 1/2 m2v2
2 = 1/2 m1v1f
2 + 1/2 m2v2f
2
Simplify
m1 ( v12 - v1f2 ) = m2 ( v2f2 - v22 ) ...... #1
Now for momentum
Pi = Pf
m1v1 + m2v2 = m1v1f + m2v2f
Simplify
m1 ( v1 - v1f ) = m2 ( v2f - v2 ) ....... #2
Divide #1 by #2; remember to factor the differnce or squares in #1; masses will cancel , results:
v1 + v1f = v2f + v2
v2f = v1 + v1f - v2
Substitute into #2; solve for v1f :
v1f = (m1-m2 / m1 + m2 )v1 + ( 2m2 / m1 + m2 ) v2
Likewise,
v2f = ( 2m1 / m1 + m2 ) v1 - ( m1 - m2 / m1 + m2 ) v2
So sub the given:
v1f = 1.56 m/s and v2f = 2.99 m/s
The answers make sense; the smaller mass should be moving slower after hitting a mass ten times larger, and the larger mass will get just a little boost in speed after being hit by the small mass.