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?

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:

[tex]p_0=p_d+p_s[/tex]

Where [tex]p_0[/tex] is the momentum of Dan and the skateboard before the jump, [tex]p_d[/tex] is the momentum of Dan after the jump and [tex]p_s[/tex] is the momentum of the skateboard after the jump.

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

[tex](m_d+m_s)v_0=m_dv_d+m_sv_s[/tex]

Solving for Dan's final speed [tex]v_d[/tex] and computing, we get:

[tex]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[/tex]

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

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 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?