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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The earths atmosphere is made up of nitrogen and oxygensolids turning into gases is called sublimation.
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:
[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.