A 39 kg child stands at rest on ice skates. She catches a 1.0 kg ball moving horizontally at 9.5 m/s. What is her speed after she's caught the ball?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A child with a mass of 39 kg stands at rest on ice skates. She catches a 1.0 kg ball moving horizontally at 9.5 m/s.

Let the speed of the child after the ball has been caught be s. The law of conservation of momentum states that the total momentum in the system is a constant. The total momentum initially is equal to the total final momentum.

Initially the total momentum of the ball and the girl is 1*9.5 + 39*0 = 9.5. The total final momentum is (39+1)*s

This gives 40s = 9.5

=> s = 9.5/40 = 0.2375 m/s

The speed of the girl after the she catches the ball is 0.2375 m/s.

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