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A rocket of 6000kg mass is set for vertical firing. If the exhaust speed of gases is 1000m/s, the rate of mass of gas ejected to supply a thrust (force) needed to give the rocket an initial upward acceleration of 20.2m/s² is

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150 kg/s

180 kg/s

160 kg/s

28 kg/s

answer is B.

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Detailed Solution

$\begin{array}{l} M (g + a) = V_{r} (\frac{dm}{dt}) \\ 6000 [9 .8 + 20 .2] = (1000) (\frac{dm}{dt}) \\ (6000) (30) = (1000) (\frac{dm}{dt}) \\ \Rightarrow \frac{dm}{dt} = 180 kg / s \end{array}$

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