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A person P on a cart on rails is receiving packages from people standing on a stationary platform. Assume that person P and the cart have a combined weight of 350 lb and start from rest. In addition suppose that a person { P }_{ A } throws a package A weighing 60 lb, which is received by person P with a horizontal speed { \upsilon }_{ A } = 4.5 ft/s. After person P has received the package from person { P }_{ A }, a second person { P }_{ B } throws a package B weighing 80 lb, which is received by person P with a horizontal speed relative to P and in the same direction as the velocity of P of 5.25 ft/s. Determine the final velocity of the person P and the cart. Neglect any friction or air resistance acting on P and the cart.

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