A rocket has total mass Mi 5 360 kg, including Mf 5 330 kg

Chapter 9, Problem 64

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A rocket has total mass Mi 5 360 kg, including Mf 5 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x 5 0, turns on its engine at time t 5 0, and puts out exhaust with relative speed ve 5 1 500 m/s at the constant rate k 5 2.50 kg/s. The fuel will last for a burn time of Tb 5 Mf/k 5 330 kg/(2.5 kg/s) 5 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by v 1t2 5 2ve lna1 2 kt Mi b (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is a1t2 5 kve Mi 2 kt (d) Graph the acceleration as a function of time. (e) Show that the position of the rocket is x1t2 5 ve a Mi k 2 tb ln a1 2 kt Mi b 1 vet (f) Graph the position during the burn as a function of time.

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