**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*.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Push-Away Problems concept. You can view video lessons to learn Push-Away Problems. Or if you need more Push-Away Problems practice, you can also practice Push-Away Problems practice problems.