**Part A**

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

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

Express the speed in terms of v_{c} and v_{b}.

Part B

What is the speed v_{b} of the ball (relative to the ground) while it is in the air?

Express your answer in terms of m_{ball}, m_{cart}, and *u*.

Part C

What is Chuck's speed v_{c} (relative to the ground) after he throws the ball?

Express your answer 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 Intro to Conservation of Momentum concept. You can view video lessons to learn Intro to Conservation of Momentum. Or if you need more Intro to Conservation of Momentum practice, you can also practice Intro to Conservation of Momentum practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Barthelemy's class at UTAH.