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Q.

A rocket of initial mass 6000 kg ejects mass at a constant rate of 16 kg/s with constant relative speed of 11 km/s. What is the acceleration of the rocket (in m/s²) a minute after the blast? Neglect gravity. (round off to nearest integer)

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answer is 35.

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Detailed Solution

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Given, initial mass of the rocket m₀ = 6000 kg and dm/dt = 16 kg/s
The mass of the rocket after 1 minute of the blast
$m = m_{0} - (\frac{dm}{dt}) t$
= 6000 - 16 x 60
= 5040 kg.
The acceleration of the rocket is given by $a = \frac{v_{r}}{m} (\frac{dm}{dt}) - g$
$= \frac{11000}{5040} \times 16 - 0$
= 34.92 m/s².

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