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Question

A rocket with an initial mass of 1000 kg is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 10 kg per second. The burnt matter is ejected vertically downwards with a speed of 2000 m/s relative to the rocket. If burning ceases after one minute, the maximum velocity of the rocket is

A
4000.6 m/s
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B
2500.4 m/s
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C
4500.2 m/s
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D
1232.6 m/s
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Solution

The correct option is D 1232.6 m/s
Given, initial mass of rocket, m0=1000 kg
Initial speed u=0
Rate of burning of fuel =10 kg/s
Speed of burnt matter with respect to rocket vr=2000 m/s
time of burning of fuel, t=1 minute=60 s


Final mass of rocket after 60 sec
m=100010×60
m=400 kg

We know that,
v=ugt+vrln(m0m)
v=010×60+2000ln(1000400)
v=600+1832.6
v=1232.6 m/s
The maximum velocity of rocket is 1232.6 m/s

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