Question

for 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 an acceleration 4.9 m/s2
will be

Answer 1

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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 an acceleration 4.9 m/s2  will be?

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${Relative \:velocity \:of \:exhaust \:gas \:\bold{V=2 \:km/s=2000\: m/s}}$

${Thrust\: force\:\bold{F_t = V\frac{dm}{dt} =2000\times\frac{dm}{dt} }$

${Acceleration\: \: \bold{a=4.9 m/s^{2}}$

$Mass \:of\: rocket\: \bold{M=1000\: kg}$

${Using\:\:\bold{Ma = F_t \:- \:Mg}}$

${Or\:\bold{ 1000\times 4.9=2000\times\frac{dm}{dt} -1000\times10}}$

$⟹ \bold{\frac{dm}{dt}} =\bold\green{{7.35kg/s}}$

Answer = 7.35kg/s

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