Dan's Momentum Change: 4m/s to Ground Zero

[trailblaza247]

Homework Statement

dan is gliding on his sb at 4m/s. he suddenly jumps backward off his sb, kicking the sb foward at 8m/s. how fast is dan going as his feet hit the ground? dan's mass is 50kg and the sb's mass is 5kg

Homework Equations

The Attempt at a Solution

 

[mbrmbrg]

Welcome aboard!

Do you have any thoughts on this problem at all? Concepts that may prove useful? Equations that relate what you know with what you're looking for?

 

[m2003]

The concept of momentum change is essential in understanding the motion of objects in physics. In this scenario, Dan's initial momentum while gliding on his skateboard is given by the product of his mass (50kg) and velocity (4m/s), which equals to 200kg*m/s. When he jumps backward off the skateboard, he exerts a force on the skateboard, causing it to accelerate forward. The final momentum of the skateboard can be calculated by multiplying its mass (5kg) with the new velocity (8m/s), resulting in a final momentum of 40kg*m/s.

According to the law of conservation of momentum, the total momentum of the system (Dan and the skateboard) remains constant. Therefore, the total momentum before and after the jump must be equal. This can be expressed mathematically as:

Initial momentum = Final momentum

(50kg * 4m/s) = (50kg + 5kg) * V

Solving for V, we get a final velocity of 3.64m/s for Dan as he hits the ground. This means that Dan's momentum has decreased from 200kg*m/s to 182kg*m/s, due to the forward momentum of the skateboard.

In conclusion, Dan's momentum change can be calculated by subtracting his initial momentum from his final momentum, which gives a change of 18kg*m/s. This change in momentum is equal to the impulse exerted on Dan by the skateboard, and it results in a final velocity of 3.64m/s for Dan as he hits the ground.