Catching a Ball on Ice Olaf is standing on a sheet of ice that covers the footba

Question

Catching a Ball on Ice 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 traveling horizontally at 10.7 m/s. Olaf's mass is 71.0 kg .(Figure 1) If Olaf catches the ball, with what speed V_f do Olaf and the ball move afterward? Express your answer numerically in meters per second. If the ball hits Olaf and bounces off his chest horizontally at 8.30 m/s in the opposite direction, what is his speed V_f after the collision? Express your answer numerically in meters per second.

Explanation / Answer

PART A

Momentum is conserved, so the momentum before and after Olaf catches the ball will be the same. Before Olaf catches the ball, the momentum is (mass * velocity= 0.400 * 10.7= 4.28 kg·m/s. This won’t change after Olaf catches the ball, so we can solve for the velocity:

= m * v
4.28 = (0.400 + 71.0) * v
4.28 = 71.4 * v
v = 0.0599 m/s answer

Part B

In Part A we saw that the total momentum is 4.28 kg·m/s. This will stay the same after the collision. Since the ball will be moving backwards (negative) at 8.30 m/s, it’s momentum after the collision is (8.30 * 0.400) =3.32 kg·m/s. So we can solve for Olaf’s momentum:

Olaf = 4.28 – ball
Olaf = 4.28 – (- 3.32)
Olaf = 7.6

Now we can solve for Olaf’s velocity:

= m * v
7.6 = 71 * v
v = 0.107 m/s answer

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