Physics Question- Momentum and Impulse

Question

A 52 kg girl rides on a 2.6 kg skateboard. The girl on the skateboard moves at 1.3 m/s. If the girl jumps off the skateboard backwards with a velocity of 1.6 m/s, how fast does the skateboard roll away?

Answer 1

This deals with conservation of momentum.

We start with the girl and the skateboard moving together. The total mass is 54.6kg and the velocity is 1.3 m/sec. Therefore, the momentum is 54.6 * 1.3 = 70.98.

When the girl pushes off of the skateboard, she has a momentum of 52 * -1.6 = -83.2. The net momentum must be 70.98, so the skateboard has to continue with a momentum of 70.98 + 83.2 = 154.18.

The velocity of the skateboard will be 154.18 / 2.6 = 59.3