Question

Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his cart, mcart, 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 mball 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 vc. The speed of the thrown ball relative to the ground is vb. 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 vj. When answering the questions in this problem, keep the following in mind: The original mass mcart 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.

Answer 1

(a) Find the relative speed between Chuck and the ball after Chuck has thrown the ball

Answer-

if two objects are moving in opposite directions(either toward each other or away from each other), the relative speed between them is equal to the sum of their speeds with respect to the ground

(b) What is the speed of the ball v_b (relative to the ground) while it is in the air?Express in terms of and u

Answer-

Initial momentum (before the ball is thrown) = Final momentum (after the ball is thrown)

Initial momentum =

Since chuck , jackie and ball are at rest

Hence final momentum =

(c) What is Chuck's speed (relative to the ground) after he throws the ball? Express in terms of and

Answer -

(d) Find Jackie's speed (relative to the ground) after she catches the ball, in terms of .Express in terms of and

answer-

Initial momentum ( before jackie catches the call) = Final momentum ( after the ball is caught)

Just before Jackie catches the ball, the momentum of the system consisting of Jackie, her cart, and the ball is equal to the momentum of the ball as it flies through the air:

Hence, initial momentum

final momentum =

(e) Find Jackie's speed (relative to the ground) after she catches the ball, in terms of . Express in terms of   and u.

Answer-

From part (b) and (d),