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  4. For a rocket propulsion velocity of exhaust gases relative to rocket is 2 km / s. If mass of rocket system is 1000 kg, then the rate of fuel consumption for a rocket to rise up with acceleration 4.9 m / s 2 will be :

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Q. For a rocket propulsion velocity of exhaust gases relative to rocket is $2 km / s$. If mass of rocket system is $1000 kg$, then the rate of fuel consumption for a rocket to rise up with acceleration $4.9 m / s ^{2}$ will be :

Laws of Motion

Solution:

Here, thrust $= v \frac{ dm }{ dt }=(2000) \frac{ dm }{ dt }$
For rocket, $v \frac{ dm }{ dt }= m ( g + a )$
$\Rightarrow 2000 \frac{ dm }{ dt }=1000(9.8+4.9)$
$\Rightarrow \frac{ dm }{ dt }=7.35 kg / s$