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Question

A rocket with an initial mass of M=2000 kg is launched vertically upwards from rest, under gravity. The burnt matter is ejected vertically downwards with a speed of 4000 m/s relative to the rocket. Velocity of the rocket after 60 seconds is 2000 m/s. Find the mass of rocket gas ejected in 60 seconds. [Take g=10 m/s2]

A
420.62 kg
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B
955.86 kg
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C
590.62 kg
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D
500.92 kg
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Solution

The correct option is B 955.86 kg
Given,
Mass of rocket initially, M=2000 kg
Burning matter ejected with a speed of vr=4000 m/s
Initial velocity of rocket u=0
Velocity of rocket after 60 seconds V=2000 m/s

Mass of rocket after 60 sec,
m=Mμt=2000μ×60
Using the velocity equation, V=ugt+vrln(Mm)
2000=010×60+4000ln(2000200060μ)
or μ=15.931 kg/s
Therefore, mass ejected in 60 seconds =μ×60
=955.86 kg

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