You axe standing on a sheet of ice that covers the football stadium parking lot

Question

You axe standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.400-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. (a) If you catch the ball, with what speed do you and the ball move afterward? (b) If the ball hits you and bounces off your chest, so afterward it is moving horizontally at 8.00 m/s in the opposite direction, what is your speed after the collision?

Explanation / Answer

Applying law of conservation of momentum in this case.

Case A: when you catch the ball the total mass will be mass of your body and mass of the ball.

So Mt = 70 + 0.4 = 70.4 kg

Say Mass of ice Mi = 0.4 kg,

Speed with which Mi is travelling be say V1

given V1 = 10m/s

Speed with which we move forward be V2

Applying law of coservation of momentum

M1 V1 = Mt V2

0.4 * 10 = 70.4 * V2

Speed with which you and ball move forward after catchingis V2 = 0.0568 m/s

Case B:

When the ball bounces off it has a greater change in momentum and you acquire a greater final speed.

initial = 0.4 x 10.5 = 4.2 kgm/s
final = (70kg x V) + (0.4kg x 8) = 70V - 3.2

Intial = Final (Law of Conservation of momentum)

4.2 = 70*V - 3.2

70*V = 7.4

V = 0.10571 m/s

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