Speed and magnitude of velocity

AI Thread Summary
The discussion revolves around a physics homework problem involving two individuals, Chuck and Jackie, who throw and catch a ball while standing on frictionless carts. The main focus is on understanding the conservation of momentum and the relationship between their speeds before and after the ball is thrown. The participant expresses uncertainty about how to incorporate initial velocities into their calculations and seeks clarification on the correct application of momentum conservation principles. Additionally, there is a mention of exploring the relationship between the kinetic energies of the carts and the ball. The thread highlights the complexities of analyzing motion in a system with multiple moving parts.
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Homework Statement


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.





Homework Equations





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!

Please help me. Thanks a lot for your time and effort!
 
Physics news on Phys.org
How about a relationship between kinetic energies

(mcart)(vcart)2 and (mball)(vball)2.
 

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