Question

Dan is gliding on his skateboard at 4.0m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0m/s. How fast is Dan going as his feet hit the ground? Dan's mass is 50kg and his skateboard's mass is 5.0kg.

Answer 1

Dan's speed as his feet hit the ground is 3.6 m/s backward, determined by using the conservation of momentum and the given masses and velocities before and after he jumps off the skateboard.

Step-by-step explanation:

To determine how fast Dan is going as his feet hit the ground after jumping off the skateboard, we can use the principle of conservation of momentum. Since there are no external forces acting on the system, the total momentum before and after Dan jumps must be the same.

Dan and the skateboard are moving together at 4.0m/s before the jump. The total initial momentum is the sum of the momentum of Dan and his skateboard:

Momentum_Dan = mass_Dan × velocity_Dan = 50kg × 4.0m/s = 200kg·m/s

Momentum_skateboard = mass_skateboard × velocity_skateboard = 5.0kg × 4.0m/s = 20kg·m/s

Total initial momentum = Momentum_Dan + Momentum_skateboard = (200 + 20) kg·m/s = 220kg·m/s moves forward at 8.0m/s. Its momentum is:

Momentum_skateboard (final) = mass_skateboard × velocity_skateboard (final) = 5.0kg × 8.0m/s = 40kg·m/s

To find Dan's velocity after the jump, we use the conservation of momentum:

Total initial momentum = Momentum_Dan (final) + Momentum_skateboard (final)

220kg·m/s = mass_Dan × velocity_Dan (final) + 40kg·m/s

Dan's final momentum is therefore:

Momentum_Dan (final) = 220kg·m/s - 40kg·m/s = 180kg·m/s

Now we can solve for Dan's final velocity:

velocity_Dan (final) = Momentum_Dan (final) / mass_Dan = 180kg·m/s / 50kg = 3.6m/s

This is the speed at which Dan is moving backward as his feet hit the ground.