Paper 4, Section I, C

Dynamics and Relativity | Part IA, 2021

A trolley travels with initial speed v0v_{0} along a frictionless, horizontal, linear track. It slows down by ejecting gas in the direction of motion. The gas is emitted at a constant mass ejection rate α\alpha and with constant speed uu relative to the trolley. The trolley and its supply of gas initially have a combined mass of m0m_{0}. How much time is spent ejecting gas before the trolley stops? [Assume that the trolley carries sufficient gas.]

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