Chuck end Jackie stand on separate carts, both of which can slide without fricti

Question

Chuck end Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his cart, m_east, 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 bal 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. The speed relative to the ground is v_b. The speed of the thrown the ball his speed relative to the ground is v_b. Jackie catches the ball when it reaches her, and she and her cart begin to move. Jeckie's speed relative to the ground after she catches the ball is v_j. When answering the question this problem, keep the following in mind: The original mass m_cart of Chuck and his cert does not include the mass of the ball The speed of on object is the magnitude of its velocity. An object speed will always be a nonnegative quantity. Find the relative speed u between Chuck and the ball after Chuck has thrown the ball Express the speed in terms of v_e and v_b What is the speed of the ball (relative to the ground) while it is in the air? What is Chuck s speed v_c relative to the ground) after ho throws the belt?

Explanation / Answer

(a) Here we will have to calculate how fast Chuck and the ball are moving away from each other. So, we will have to calculate the relative speed between the two

u = vc + vb

(b) initial momentum of Chuck, cart and the ball pi = 0, as they all are at rest

Final momentum of Chuck, cart and the ball pf = 0 + mcart (-vc) + mball vb

pf = -mcart vc + mball vb

from part (a) we have vc = u - vb

pf = -mcart (u - vb) + mball vb

pf = -mcart u + (mcart + mball ) vb

Now, by conservtion of momentum pi = pf

0 = -mcart u + (mcart + mball ) vb

vb = (mcart u) / (mcart + mball )

(c) From part (a) we have vc = u - vb

Using value of vb from part (b), we get

vc = u - { (mcart u) / (mcart + mball ) }

vc = (mball u) / (mcart + mball )

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