Question

A large blue marble of mass 3.5 g is moving to the right with a velocity of 15 cm/s. The large marble hits a small red marble of mass 1.2 g that is moving to the right with a velocity of 3.5 cm/s. After the collision, the blue marble moves to the right with a velocity of 5.5 cm/s.

What is the magnitude of the final velocity of the red marble?

9.2 cm/s
14 cm/s
24 cm/s
31 cm/s

Answer 1

Use conservation of momentum:

m1 v1i + m2 v2i = m1 v1f + m2 v2f

Solve for v2f:
v2f = [m1(v1i − v1f) + m2 v2i] / m2
= [3.5(15 − 5.5) + 1.2(3.5)] / 1.2
= [3.5(9.5) + 4.2] / 1.2
= (33.25 + 4.2) / 1.2 ≈ 31.2 cm/s

Magnitude ≈ 31 cm/s.