Question

Dan is gliding on his skateboard at 2.00 m/s. He suddenly jumps backwardoff the skateboard, kicking the skateboard forward at 8.00 m/s (as measured by an observeron the ground). Dan's mass is 60.0 kg and the skateboard's mass is7.00 kg.

How fast is Dan going as his feet hit the ground?

Answer 1

Dan is going about 1.30m/s fast as his feet hit the ground.

Step-by-step explanation:

From the conservation of linear momentum, we know that the momentum of the system must be equal before and after Dan jumps. So, we can express this with the equation:

`p_0=p_d+p_s`

Where
`p_0` is the momentum of Dan and the skateboard before the jump,
`p_d` is the momentum of Dan after the jump and
`p_s` is the momentum of the skateboard after the jump.

Now, as momentum is equal to mass times velocity, we can write the equation as:

`(m_d+m_s)v_0=m_dv_d+m_sv_s`

Solving for Dan's final speed
`v_d` and computing, we get:

`v_d=((m_d+m_s)v_0-m_sv_s)/(m_d)\\\\v_d=((60.0kg+7.00kg)(2.00m/s)-(7.00kg)(8.00m/s))/(60.0kg)\\ \\v_d=1.30m/s`

It means that Dan has a speed of about 1.30m/s when his feet hit the ground.