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Question

A rocket of mass 120 kg has 280 kg of fuel is ready for the take off. The relative exhaust velocity of the fuel is 1.8 km/s and the rate of consumption of the fuel is 2 kg/s. Calculate the ultimate vertical speed gained by the rocket. (Take g=9.8 m/s2)

A
3.54 km/s
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B
1.79 km/s
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C
0.795 km/s
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D
0 km/s
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Solution

The correct option is C 0.795 km/s
Given,
Mass of the rocket without fuel =120 kg
Mass of the fuel in the rocket =280 kg
Total initial mass of the rocket m0=400 kg
Exhaust velocity of the fuel (vr)=1.8 km/s
Rate of consumption of fuel μ=2 kg/s
Then, time at which the fuel will be finished (t)=2802=140 s

Final velocity of the rocket at t=140 s
v=ugt+vrln(m0m)
=09.8×140+1.8×103ln(400120)
=1372+2167
=795 m/s=0.795 km/s

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