# Speed and magnitude of velocity

1. Sep 22, 2007

### mit_hacker

1. The problem statement, all variables and given/known data
Hello everyone! There is this one question that I do not have the answer to so I was just wondering if anyone could check my solutions and answers and let me know whether I was correct or not. Thank-you for your time!!

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:

1. The original mass m_cart 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.

2. Relevant equations

3. The attempt at a solution

(a) The relative VELOCITY will be the difference in the two velocities (i.e.) vb-va. But since we are asked the speed of them, we will have to add them up because they are in oppositte direction so actually, the velocity will also be vb+va.

(b) By law of conservation of momentum, (mcart)(vcart) = (mball)(vball). But I don't know how to bring u into the picture.

(c) Same problem here!!

(d) By law of conservation of momentum,

vj = (mcart)(vcart) / (mj)

(e) Same problem here!!