Question

Find rate of ejection of fuel so that the rocket is just launched from its launching pad.
Mass of rocket is 10000 kg and Vr = 100m/sec​

Answer 1

$\huge {\orange {\underline{ \overline{ \boxed{ \mathbb{ \blue{ANSWER}}}}}}}$

$\sf{ \green{ \underline{ \underline{GIVEN :}}}}$

• Mass of the rocket = 10,000 kg
• $\sf V_r \:$(Velocity of fuel ejecting out with respect to rocket) = 100m/ sec.

$\sf{ \green{ \underline{ \underline{TO \: \: FIND :}}}}$

Rate of ejection of fuel.

$\sf{ \green{ \underline{ \underline{SOLUTION :}}}}$

For just launching the rocket the minimum thrush required is equal to the downward force acting due to gravity.

By applying the formula, we get

$\boxed {\sf{ \red{ \mid \: F_{thrush} \: \mid \: = \: mg}}}$

$\implies \: \sf \: V_r \times \frac{dm}{dt} = \: mg$

[On putting the required values]

$\implies \: \sf \:100 \times \frac{dm}{dt} = \: 10000 \times 10$

$\implies \: \sf \:1 \cancel{00} \times \frac{dm}{dt} = \: 100 \cancel{00} \times 10$

$\implies \: \sf \frac{dm}{dt} = \: 100 \times 10$

$\implies \: \sf \frac{dm}{dt} = \: 1000 \: kg / sec$

$\boxed {\therefore{ \sf{ \red{The \: rate \: of \: ejection \: of \: fuel \: is \: 1000 \: Kg/sec.}}}}</p><p>$

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