A 30 kg girl and a 25 kg boy face each other on friction-free roller skates. The girl pushes the boy, who moves away at a speed of 1.0 m/s. What is the girl's speed?

Answer: 4m/s

Explanation:

Mass of girl = m1 = 30kg

Mass of boy = m2 = 25kg

Resultant speed after collision = 1.0m/s

Speed of girl = v1

Speed of boy = v2

Momentum = mass * velocity

m1v1 - m2v2 = mv

30v1 - 25v2 = 1*m

30v1 - 25v2 = m

v1 = (m + 25v2) / 30 ... eqn 1

but m1 - m2 = m

m = 30 - 25 = 5kg

v1 = (5 + 25v2) / 30 ... eqn 2

v1-v2 = 1m/s

v2 = (v1 - 1) m/s

Substitute for v2 in eqn 2

v1 = [5 + 25 (v1 - 1) ]/30

30v1 = 5 + 25v1 - 25

30v1 - 25v1 = - 20

5v1 = - 20

v1 = - 4m/s

Because she moved in an opposite direction to the boy, the negative sign is featured on her speed