**Part A**

From the conservation of linear momentum:

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

m_{ball}v_{b} = (m_{ball} + m_{cart})v_{j}

Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his cart,m_{cart}, 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 m_{ball} 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 v_{c}. The speed of the thrown ball relative to the ground is v_{b}.

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 v_{j}.

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

The original mass m

_{cart}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 A

Find Jackie's speed v_{j} (relative to the ground) after she catches the ball, in terms of v_{b}.

Express v_{j} in terms of m_{ball}, m_{cart}, and v_{b}.

Part B

Find Jackie's speed v_{j} (relative to the ground) after she catches the ball, in terms of *u (Given that v _{b} = m_{cart }u/m_{cart} + m_{ball})*

Express v_{j} in terms of m_{ball}, m_{cart}, and *u*.

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