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 11.3 m/s . Olaf's mass is 73.0 kg .(Figure 1)

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

2. If the ball hits Olaf and bounces off his chest horizontally at 8.50 m/s in the opposite direction, what is his speed vf after the collision?

Explanation / Answer

we can solve both parts by using conservation of momentum.

a) momentum before Olaf catches the ball will be = 0.4 Kg * 11.3 m/s = 4.52 Kg.m/s

momentum after Olaf catches the ball will be = (0.4 + 73) * vf

73.4 * vf= 4.52

hence speed vf do Olaf and the ball move afterward will be 0.0615 m/s = 6.15 cm/s

b)

inital momentum will be same in this case as well 0.4 Kg * 11.3 m/s = 4.52 Kg.m/s

final momentum will be calculated seperated for ball and olaf

momentum of ball will = 0.4 * (-8.5) = - 3.4 Kg.m/s (negative as ball moves backward)

momentum of olaf will be = 73 * vo

vo is speed of olaf after collision

now 4.52 = 73*vo + (-3.4)

vo= 0.1084 m/s = 10.84 cm/s

speed vf after the collision 10.84 cm/s

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