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31 October, 00:35

Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground? Dan's mass is 50 kg and the skateboard's mass is 5.0 kg?

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  1. 31 October, 00:50
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    3.6 m/s

    Explanation:

    From the law of conservation of momentum,

    Total momentum before jump = Total momentum after jump

    Note: Before Dan jump off the skateboard, they where both moving with the same velocity

    u (m+m') = mv+m'v' ... Equation 1

    Where m = Dan's mass, m' = mass of the skateboard, u = common velocity before the jump, v = Dan's final velocity, v' = The final velocity of the skateboard.

    make v the subject of the equation

    v = [u (m+m') - m'v') ]/m ... Equation 2

    Given: u = 4.0 m/s, m = 50 kg, m' = 5 kg, v' = 8 m/s

    Substitute into equation 2

    v = [4 (50+5) - (5*8) ]/50

    v = (220-40) / 50

    v = 180/50

    v = 3.6 m/s
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