Question

A rocket is launched with gas ejection speed of $400\text{m/s}$ and acceleration of $25{\text{m/s}}^2$. If mass of the rocket is $4000\text{kg}$, what will be the rate of consumption of the fuel?
(Take $g=10{\text{m/s}}^2$)

• A. $250\text{kg/s}$
• B. $300\text{kg/s}$
• C. $400\text{kg/s}$
• D. $350\text{kg/s}$

Answer 1

The correct option is D $350\text{kg/s}$

Given,
Mass of the rocket, $M=4000\text{kg}$
Gases ejection speed, $v=400\text{m/s}$
Acceleration of rocket, $a=25{\text{m/s}}^2$
As we know,
$v.\frac{dm}{dt}-Mg=Ma$
$400\times \frac{dm}{dt}-4000\times 10=\left(4000\right)\times \left(25\right)$
$\frac{dm}{dt}=350\text{kg/s}$