# 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 Jackie's speed vj (relative to the ground) after she catches the ball, in terms of vb.Express vj in terms of mball, mcart, and vb.Part BFind Jackie's speed vj (relative to the ground) after she catches the ball, in terms of u (Given that vb = mcart u/mcart + mball)Express vj in terms of mball, mcart, and u.

###### FREE Expert Solution

Part A

From the conservation of linear momentum:

The initial momentum before Jackie catches the ball =  the final momentum after Jackie catches the ball.

mballvb = (mball + mcart)vj

###### 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 Jackie's speed vj (relative to the ground) after she catches the ball, in terms of vb.

Express vj in terms of mball, mcart, and vb.

Part B

Find Jackie's speed vj (relative to the ground) after she catches the ball, in terms of u (Given that vb = mcart u/mcart + mball)

Express vj in terms of mball, mcart, and u.