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A Rocket having initial mass $5 \times 10^{6} kg, which includes mass of fuel of mass 4 \times 10^{6} kg is ejecting$ gas with velocity 4000 m/s relative to Rocket. Then what will be the velocity of the Rocket when entire fuel finishes? $(\ln (5) = 1.6094)$

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6438 m/s

4500 m/s

3785 m/s

4000 m/s

answer is A.

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Detailed Solution

$V = u_{r e c .} \ln (\frac{m}{M})$

$V = 4000 . \ln (\frac{5 \times 10^{6}}{1 \times 10^{6}})$

V = 4000 ln(5)

V = 6437.75 m/s

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