## Mastering Physics Solutions: Catching a Ball on Ice

Catching a Ball on Ice

Part A = 6.72 cm/s
Part B = 11.0 cm/s

Solution Below:

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 11.7 m/s. Olaf’s mass is 69.2 kg.

Part A

If Olaf catches the ball, with what speed vf do Olaf and the ball move afterward?

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 * 11.7) 4.68 kg·m/s. This won’t change after Olaf catches the ball, so we can solve for the velocity:

ρ = m * v
4.68 = (0.400 + 69.2) * v
4.68 = 69.6 * v
v = 0.0672 m/s

For some reason, Mastering Physics wants the answer in centimeters per second. So just multiply by 100:

vf = 6.72 cm/s

6.72 cm/s

Part B

If the ball hits Olaf and bounces off his chest horizontally at 7.40 m/s in the opposite direction, what is his speed after the collision?

Remember momentum is conserved. In Part A we saw that the total momentum is (mass * velocity, or 0.400 * 11.7) 4.68 kg·m/s. This will stay the same after the collision. Since the ball will be moving backwards (negative) at 7.40 m/s, it’s momentum after the collision is (7.40 * 0.400) 2.96 kg·m/s. So we can solve for Olaf’s momentum:

ρOlaf = 4.68 – ρball
ρOlaf = 4.68 – (- 2.96)
ρOlaf = 7.64

Now we can solve for Olaf’s velocity:

ρ = m * v
7.64 = 69.2 * v
v = 0.110 m/s

For some reason, Mastering Physics wants this in centimeters per second, so just multiply by 100. The answer is 11.0 cm/s

11.0 cm/s

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