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Question

A rocket with an initial mass m=2000 kg is launched vertically upwards. The rocket burns fuel at the rate of 20 kg/s. The burnt material is ejected vertically downwards with a speed of 4000 m/s relative to the rocket. If burning stops after 30 seconds, find the maximum velocity of the rocket. (Take g=10 m/s2 )

A
0 m/s
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B
4515.9 m/s
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C
1126.7 m/s
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D
300 m/s
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Solution

The correct option is C 1126.7 m/s
Given,
Initial mass of Rocket m0=2000 kg
Rocket fuel burning rate μ=20 kg/s
Burnt matter ejection speed vr=4000 m/s
From velocity equation v=ugt+vrln(mom)
Here u=0, initially. At t=30 sec,
v=010×30+4000×ln(2000200020×30)
(m=m0μt)
v=1126.7 m/s

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