A rocket of mass 20kg has 180 kg of fuel. The exhaust velocity of fuel is 1.6 km/sec. Calculate the ultimate velocity of the rocket gained, when the rate of consumption of the fuel is 2kg/sec. (neglect gravity)

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3.7 km/sec

2 km/sec

10 km/sec

5 km/sec

answer is A.

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Detailed Solution

m0 = 20 + 180 = 200kg mdvdt=0 +-urdmdt ⇒∫0vdv = -ur∫mimf 1mdm ⇒v = ur ln mimf = 3.7m/s

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