Paper 4, Section I, C

A trolley travels with initial speed $v_{0}$ 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 $\alpha$ and with constant speed $u$ relative to the trolley. The trolley and its supply of gas initially have a combined mass of $m_{0}$. How much time is spent ejecting gas before the trolley stops? [Assume that the trolley carries sufficient gas.]

*Typos? Please submit corrections to this page on GitHub.*