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Question

A rocket of mass 3500 kg has to achieve a velocity of 1000 m/s over a launch time of 10 minutes. The nozzle of the rocket is designed to let out exhaust gases at a velocity of 300 m/s w.r.t the rocket. What is the amount of fuel that is consumed during the launch?

A
81660 kg
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B
66666.66 kg
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C
90000 kg
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D
88666.66 kg
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Solution

The correct option is A 81660 kg
Initial mass of the rocket =m=3500 kg
Acceleration of the rocket over the lauch time
=a=vft=1000 m/s10×60 s=1.666 m/s2
Relative velocity of exhaust gases vr=300 m/s

We have the equation,
vrdmdtmg=ma
300×dmdt3500×10=3500×1.666
dmdt=3500×11.666300=136.10 kg/s
Amount of fuel consumed over 10 minutes
M=136.10×10×60=81660 kg
Hence 81660 kg is consumed over ten minutes.

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