Intro to Conservation of Momentum Video Lessons

Concept

# Problem: Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his cart, mcart, is identical to the combined mass of Jackie and her cart. Initially, Chuck and Jackie and their carts are at rest.Chuck then picks up a ball of mass mball and throws it to Jackie, who catches it. Assume that the ball travels in a straight line parallel to the ground (ignore the effect of gravity). After Chuck throws the ball, his speed relative to the ground is vc. The speed of the thrown ball relative to the ground is vb.Jackie catches the ball when it reaches her, and she and her cart begin to move. Jackie's speed relative to the ground after she catches the ball is vj.When answering the questions in this problem, keep the following in mind:The original mass mcart of Chuck and his cart does not include the mass of the ball.The speed of an object is the magnitude of its velocity. An object's speed will always be a nonnegative quantity.Part AFind the relative speed u between Chuck and the ball after Chuck has thrown the ball.Express the speed in terms of vc and vb.Part BWhat is the speed vb of the ball (relative to the ground) while it is in the air?Express your answer in terms of mball, mcart, and u.Part CWhat is Chuck's speed vc (relative to the ground) after he throws the ball?Express your answer in terms of mball, mcart, and u.

###### FREE Expert Solution

Part A

For motion in opposite directions, the relative speed is the sum of the speeds of the objects with respect to the ground.

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###### Problem Details

Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his cart, mcart, is identical to the combined mass of Jackie and her cart. Initially, Chuck and Jackie and their carts are at rest.

Chuck then picks up a ball of mass mball and throws it to Jackie, who catches it. Assume that the ball travels in a straight line parallel to the ground (ignore the effect of gravity). After Chuck throws the ball, his speed relative to the ground is vc. The speed of the thrown ball relative to the ground is vb.

Jackie catches the ball when it reaches her, and she and her cart begin to move. Jackie's speed relative to the ground after she catches the ball is vj.

When answering the questions in this problem, keep the following in mind:

1. The original mass mcart of Chuck and his cart does not include the mass of the ball.

2. The speed of an object is the magnitude of its velocity. An object's speed will always be a nonnegative quantity.

Part A

Find the relative speed u between Chuck and the ball after Chuck has thrown the ball.

Express the speed in terms of vc and vb.

Part B

What is the speed vb of the ball (relative to the ground) while it is in the air?

Part C

What is Chuck's speed vc (relative to the ground) after he throws the ball?