When answering the questions in this problem, keep the following in mind: Chuck

Question

When answering the questions in this problem, keep the following in mind:

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 massm_balland 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 isv_c. The speed of the thrown ball relative to the ground isv_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 isv_j. When answering the questions in this problem, keep the following in mind: The original massm_cartof 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 speedubetween Chuck and the ball after Chuck has thrown the ball. Express the speed in terms ofv_candv_b. Part B What is the speedv_bof the ball (relative to the ground) while it is in the air? Express your answer in terms ofm_ball,m_cart, andu. Part C What is Chuck's speedv_c(relative to the ground) after he throws the ball? Express your answer in terms ofm_ball,m_cart, andu. Part D Find Jackie's speedv_j(relative to the ground) after she catches the ball, in terms ofv_b. Expressv_jin terms ofm_ball,m_cart, andv_b. Part E Find Jackie's speedv_j(relative to the ground) after she catches the ball, in terms ofu. Expressv_jin terms ofm_ball,m_cart, andu.

Explanation / Answer

a) Due to momentum conservation chuck and ball will move in opposite direction.

Thus, relative velocity u = v_c + v_b

b) Momentum conservation: m_cart*0 = m_cart*v_c - m_b*v_b

m_b*v_b = m_cart*v_c

v_b = (m_cart/m_b)*(u - v_b)

u/v_b - 1 = m_b/m_cart

v_b = u*m_cart/(m_b + m_cart)

c) v_c = (m_b/m_cart)*v_b

v_c = (m_b/m_cart) * u*m_cart/(m_b + m_cart)

v_c = u*m_b/(m_b + m_cart)

d) Momentum conservation: m_cart*0 + m_b*v_b = (m_cart + m_b)*v_j

v_j = v_b*m_b/(m_cart + m_b)

e) v_j = u*m_cart/(m_b + m_cart) *m_b/(m_cart + m_b)

v+j = u*m_b*m_cart/(m_cart + m_b)^2

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