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?

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