A rocket of initial mass $6000 k g$ ejects mass at a constant rate of $16 k g / s$ with constant relative speed of $11 k m / s$ . What is the acceleration of the rocket a minute after the blast? (Neglect gravity)

28.7 m / s^{2}

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34.9 m / s^{2}

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39.4 m / s^{2}

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27.8 m / s^{2}

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Solution

The correct option is B $34.9 m / s^{2}$
$v_{r} = 11 k m / s = 11000 m / s$

Thrust force on rocket is $F = v_{r} \frac{d m}{d t}$

$F = 11000 \times 16 = 17600 N$

Mass of rocket after one minute

$M = 6000 - 16 \times 60 = 5040 k g$

Acceleration of rocket is $a = \frac{F}{M} = \frac{17600}{5040} = 34.92 m / s^{2}$

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