Olaf is standing on a sheet of ice that covers the football stadium parking lot

Question

Olaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws olaf a ball of mass 0.400 kg that is travelling horizontally at 11.0 m/s. Olaf's mass is 71.9 kg. If Olaf catches the ball, with what speed do Olaf and the ball move afterward? Express your answer numerically in meters per second. If the ball hits Olaf and bounces of his chest horizontally at 7.70 m/s in the opposite direction, what is his speed v_g after the collision? Express your answer numerically in meters per second.

Explanation / Answer

Mass of ball, mb = 0.4 kg
Mass of olaf, m = 71.9 kg
Velocity of ball, vb = 11.0 m/s

Using Conservation of Momentum,
Initial Momentum = Final Momentum

As in the First case, both the ball and boy will move with same speed.

mb*vb = (m + mb) * vf
vf = mb/(m + mb) * vb
vf = (0.4)/(0.4+71.9) * 11.0
vf = 0.061 m/s
They will move together in the direction where the ball was thrown with speed, vf = 0.061 m/s

(b)
Noe Velocity of ball affter collison, vbf = - 7.7 m/s (-ve sign shows direction.)
Again,
Using Conservation of Momentum,
Initial Momentum = Final Momentum
mb*vb = m*vf + mb*vbf
0.4*11.0 = - 0.4* 7.7 + 71.9 * vf
vf = 0.104 m/s

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