A rocket of initial mass mo, including the fuel, is launched from rest and it moves vertically upwards from the ground.

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A Rocket Of Initial Mass Mo Including The Fuel Is Launched From Rest And It Moves Vertically Upwards From The Ground 1 (37.1 KiB) Viewed 87 times

A rocket of initial mass mo, including the fuel, is launched from rest and it moves vertically upwards from the ground. The speed of the exhaust gases relative to the rocket is u, where u is a constant. The mass of fuel burnt per unit time is a constant a. Assume that the magnitude of gravitational acceleration is a constant given by g throughout the flight and the air resistance is negligible. The velocity of the rocket is v when the mass of the rocket is m. Suppose that v and m satisfy the following differential equation. Convention: Upward as positive. du 9 u dm m m mo 9 (a) Show that v = (m-mo) - u In (6 marks) (b) When the mass of the rocket is m, the altitude of the rocket is y. Show that (6 marks) dy 9 (m-mo) + In dm u "(m) a? a