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 1.0 kg ball to Sarah at 4.5 m/s, while Sarah throws a 0.50 kg ball to James at 1.0 m/s. James’s throw is to the right and Sarah’s is to the left.

Part A: While the two balls are in the air, what is the speed of the cart and its riders?

Part B: While the two balls are in the air, what is the direction of the cart and its riders? (Choices are left, or right)

Part C: After the balls are caught, what is the speed of the cart and riders?

Part D: After the balls are caught, what are the direction of the cart and riders?
(Choices are left, right, or not moving)

Explanation / Answer

The total mass M = 130kg the mass of the ball thrown by james m1 =1.0kg it speed v1 = 4.5m/s the mass of the ball thrown by sarah m2 = 0.5kg it speed v2 = 1.0m/s From law of conservation of momentum m1v1 - m2v2 = Mv therefore the speed v = m1v1 - m2v2 / M = [(1)(4.5) - (0.5)(1)] / 130 = 0.0307 m/s The direction is towards left After the ball caught the riders and cart is not moving its comes to rest

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