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 0.400kg that is traveling horizontally at 10.3m/s . Olaf's mass is 66.8kg .

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

Ans: Vf= ___ m/s

Part B: If the ball hits Olaf and bounces off his chest horizontally at 7.60m/s in the opposite direction, what is his speed vf after the collision?

Ans: Vf= ____m/s

Explanation / Answer

This is a typical conservation of momentum question . You just have to equate the initial and final momentums as there is no energy loss due to friction.

Denote momentum as P.

Pi = initial momentum Mb = mass of ball

Pf = final momentum. Mo= mass of Olaf

(a) Pi = (Mb)*(Vb) = 0.4*10.3= 4.12 kgm/s

After he catches the ball the total mass is Mo + Mb

=>Pf = (Mo + Mb)*Vf = Pi

=>4.12=(66.8+0.4)*Vf

=>Vf= 0.0613 m/s

(b) Since uptill now we have been assuming that the initial direction of the ball (left in the picture) is positive , we shall continue that.

Pi = 4.12 kgm/s as before.

Now the ball moves in opposite direction at 7.6m/s

=> momentum of the ball = (0.4)*(-7.6)= -3.04 kgm/s ( -ve sign because of the opposite direction)

momentum of Olaf = (Mo)*(Vf)

=>Pf = (Mo)*(Vf) -3.04 = Pi = 4.12

=> Vf= 0.1072 m/s

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