A rocket of mass 120kg has 280kg fuel. The relative exhaust velocity of the fuel is 1.8km/s and the rate of consumption of the fuel is 2kg/s. Calculate the ultimate vertical speed gained by the rocket. (Take g=9.8m/s2)
A
3.54km/s
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B
1.79km/s
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C
0.795km/s
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D
0km/s
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Solution
The correct option is C0.795km/s Given, Mass of the rocket without fuel =120kg Mass of the fuel in the rocket =280kg ∴ Total initial mass of the rocket m0=400kg Exhaust velocity of the fuel (vr)=1.8km/s Rate of consumption of fuel μ=2kg/s Then, time at which the fuel will be finished (t)=2802=140s
Final velocity of the rocket at t=140s v=u−gt+vrln(m0m) =0−9.8×140+1.8×103ln(400120) =−1372+2167 =795m/s=0.795km/s