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A $6000 k g$ rocket set for a vertical flight. If the exhaust speed of gases is $1000 m / s$ , how much gas must be ejected per second to supply the thrust needed to give the rocket an initial upward acceleration

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$90 k g / s e c$

$60 k g / s e c$

$120 k g / s e c$

$9 k g / s e c$

answer is B.

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Detailed Solution

The upthrust must be equal to the weight of the rocket in order to have a initial upward acceleration.

$mg = u \frac{dm}{dt}$

$6000 x 10 = 1000 . \frac{dm}{dt}$

$\frac{dm}{dt} = 60 kg / s$

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