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 traveling horizontally at 10.2 m/s . Olaf's mass is 73.8 kg .(Figure 1) Part A If Olaf catches the ball, with what speed vf do Olaf and the ball move afterward? If the ball hits Olaf and bounces off his chest horizontally at 8.20 m/s in the opposite direction, what is his speed vf after the collision?

Explanation / Answer

Part A:

Remember that 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, or 0.400 * 10.2) 4.08 kg·m/s. This won’t change after Olaf catches the ball, so we can solve for the velocity:

= m * v
4.08 = (0.400 + 73.8) * v
4.08 = 74.2 * v
v = 0.055 m/s

vf = 5.5 cm/s

Part B:

Remember momentum is conserved. In Part A we saw that the total momentum is (mass * velocity, or 0.400 * 10.2) 4.08 kg·m/s. This will stay the same after the collision. Since the ball will be moving backwards (negative) at 8.20 m/s, it’s momentum after the collision is (8.20 * 0.400) 3.28 kg·m/s. So we can solve for Olaf’s momentum:

Olaf = 4.08 – ball
Olaf = 4.08 – (- 3.28)
Olaf = 7.36

Now we can solve for Olaf’s velocity:

= m * v
7.36 = 73.8 * v
v = 0.0997 m/s

vf =9.97 cm/s

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