Brittany stands at rest on a skateboard. The combined mass of Brittany and the skateboard is 62 kg. Dave tosses a 3.7-kg pumpkin to Brittany, and when she catches it, she and the skateboard begin to roll backward with a speed of 0.18 m/s.
What was the speed of the pumpkin?

3.196 m/s

Explanation:

Parameters given:

Mass of Brittany and the skateboard, M = 62 kg

Mass of pumpkin, m = 3.7 kg

Initial speed of Brittany and the skateboard, U = 0 m/s

Final velocity of Brittany, the skateboard and the pumpkin, V = v = 0.18 m/s

We can solve this problem by applying the principle of conservation of momentum.

It states that the total final momentum of a system is equal to the total initial momentum of the system.

M*U + m*u = M*V + m*v

Where u is the initial velocity of the pumpkin.

Since the final velocity of Brittany and the skateboard is equal to the final velocity of pumpkin:

M*U + m*u = (M + m) *v

Solving this to get u:

(62 * 0) + (3.7 * u) = (62 + 3.7) * 0.18

0 + 3.7u = 65.7 * 0.18

3.7u = 11.826

u = 11.826 / 3.7

u = 3.196 m/s

The initial velocity of the pumpkin was 3.196 m/s.