James and Sarah stand on a stationary cart with frictionless wheels. The total m

Question

James and Sarah stand on a stationary cart with frictionless wheels. The total mass of the cart and riders is 130 kg. At the same instant, James throws a 1.9 kg ball to Sarah at 4.7 m/s , while Sarah throws a 0.70 kg ball to James at 1.1 m/s . James’s throw is to the right and Sarah’s is to the left, both speeds are measured relative to the ground.

While the two balls are in the air, what are the speed and direction of the cart and its riders? Consider direction to the right as the positive direction and pay atention to the sign of your answer.

After the balls are caught, what is the speed of the cart and riders? Consider direction to the right as the positive direction and pay atention to the sign of your answer.

Explanation / Answer

Now applying the conservation of linear momentum for the system

1.9*4.7-0.70*1.1 +130*v =0

8.93 -0.77+130*v =0

8.16+130v =0

v =-8.16/130 =-0.0627m/s (v is the velocity of the cart along the right side)

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