A rocket, with an initial mass of 1000kg, is launched vertically upward 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. Find the velocity of the rocket in ms^-1 after 1 min of start. (Take $\ln$ 2.5 = 0.92), (g =10 ms-2)

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answer is 1240.

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Detailed Solution

$v = u - g t + v_{r} 1 n (\frac{m_{0}}{m})$

Here $u = 0, t = 60 s, g = 10 m / s^{2}, v_{r} = 2000 m / s, m_{0} = 1000 k g$ and $m = 1000 - 10 \times 60 = 400 k g$
Putting these values, we get
$v = 0 - 600 + 20001 n (\frac{1000}{400}) = 20001 n 2.5 - 600 = 1240 m / s$

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