Question

A person (mass 40.0kg) is coasting on their skateboard (mass 4.00kg) at 6.50m/s. They suddenly jump directly backward off the skateboard, kicking the skateboard forward at 12.0m/s. As soon as their feet leave the skateboard, how fast are they moving?

Answer 1

The final velocity of the person after jumping off the skateboard can be calculated using the principle of conservation of momentum.

Step-by-step explanation:

When the person jumps off the skateboard, the Law of Conservation of Momentum applies. According to this law, the total momentum before the jump is equal to the total momentum after the jump.

Let's calculate the momentum of the person-skateboard system before and after the jump:

• Before the jump: Momentum = (mass of person + mass of skateboard) x velocity of person-skateboard system
• After the jump: Momentum = (mass of person) x velocity of person + (mass of skateboard) x velocity of skateboard

Since there are no external forces acting on the system, the momentum before the jump and after the jump must be equal:

(mass of person + mass of skateboard) x 6.50m/s = (mass of person) x (final velocity of person) + (mass of skateboard) x 12.0m/s

Now we can solve this equation to find the final velocity of the person.