A 500 kg rocket is set for a vertical firing. If the exhaust speed is $250 \mathrm{~m} \mathrm{s}^{-

Question

A 500 kg rocket is set for a vertical firing. If the exhaust speed is $250 \mathrm{~m} \mathrm{s}^{-1}$, the mass of the gas ejected per second to supply the thrust needed just to overcome the weight of rocket is (Take $g = 10 \mathrm{~m/s}^2$)

Professor PC Thomas Classes · Answer

Thrust to just overcome weight: $F = Mg = 500 	imes 10 = 5000 \mathrm{~N}$. Thrust is also $F = u \frac{dm}{dt}$. Therefore, $250 \frac{dm}{dt} = 5000 \implies \frac{dm}{dt} = 20 \mathrm{~kg/s}$.