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 11.6 m/s . Olaf's mass is 72.1 kg .

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

PART B.) If the ball hits Olaf and bounces off his chest horizontally at 7.90 m/s in the opposite direction, what is his speed vf after the collision?

Explanation / Answer

Part A)

Since there is negligible friction between Olaf's feet and ice, the linear momentum is conserved before and after catching the ball.

Initial momentum = momentum of ball + momentum of Olaf

                             = (mass*velocity)ball + (mass*velocity)Olaf

                                      = (0.4*11.6) + (72.1*0)

Final momentum = momentum of ball+Olaf

                            = (massball+massOlaf)*vf

                            = (0.4+72.1)*vf

Since Initial momentum = Final momentum

           (0.4+72.1)*vf = (0.4*11.6) + (72.1*0)

           vf = 6.4*10-2 m/s

Part B)

Here again linear momentum is conserved.

The initial momentum is same as in Part A.

But Final momentum is the sum of (momentum of ball) and (momentum of Olaf)

Final momentum = massball*velocityball + massOlaf*vf

                            = 0.4*(-7.9)+72.1*vf    (velocity of ball is negative because it is in opposite direction)

Equating initial and final momenta, we get

(0.4*11.6) + (72.1*0) = 0.4*(-7.9)+72.1*vf

or vf = 0.4*(11.6+7.9)/72.1 = 0.108 m/s

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