Question

The mass of the rocket is 500 Kg and relative velocity of gas ejected out is 950 m/s with respect to rocket. determine the rate burning of the fuel in order to given the acceleration of the rocket is $20m/s^2?$

Answer 1

Given that,

Mass $m=500kg$

Velocity $v=950m/s$

Acceleration $a=20m/s^2$

We know that,

$a=\left(\frac{u}{m_0-t\frac{dm}{dt}}\right)\frac{dm}{dt}-g$

$20=\left(\frac{950}{500-1\times \frac{dm}{dt}}\right)\frac{dm}{dt}-10$

$30=\left(\frac{950}{500-x}\right)x$

Where, $x=\frac{dm}{dt}$

So,

$30=\left(\frac{950}{500-x}\right)x$

$15000-30x=950x$

$980x=15000$

$x=15.31kg/s$

$\frac{dm}{dt}=15.31kg/s$

Hence, this is the required solution