# Dan is gliding on his skateboard at 2.00 m/s. He suddenly jumps backwardoff the skateboard, kicking

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?

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

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:

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

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