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 11.8 m/s. Olaf's mass is 69.2 kg. 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 8.70 m/s in the opposite direction, what is his speed vf after the collision? Both in cm/s.

Explanation / Answer

a) .0571 m/s b) .109 m/s This is a conservation of momentum problem. The formula for this is: M1V1 + M2V2 = M1V1 + M2V2. The left side of the equation are the initial values, and the right side of the equation are the final values. For the first half of your question, the ball and Olaf stick together after colliding, so you add their masses together. So, the formula for this is: M1V1 + M2V2 = (M1 + M2)Vf Plug in your values and you get: (.4)(10) + (69.6)(0) = (.4 + 69.6)(Vf). Solve for Vf and you'll get .0571 m/s For the second part of your question, use the first formula I typed, and plug in the known values. (.4)(10) + (69.6)(0) = (.4)(-9) + (69.6)(Vf). Again, solve for Vf and you'll get .109 m/s You must notice that the ball, after hitting Olaf, travels in the opposite direction. Thus the need to use a -9 m/s, NOT a +9 m/s

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