A 500 kg rocket is set for vertical firing . The exhaust speed is 800m/s. To give an initial upward acceleration of $20m/s^2$ , the amount of gas ejected per second to supply the needed thrust will be (Take $g=10m/s^2$ )

Given : Mass of rocket (m) = 5000kg

Exhaust speed (v) = 800m/s

Acceleration of rocket (a) = $20m/s^2$

Gravitational acceleration (g) = $10m/s^2$

We know that upward force

$F=m\left(g+a\right)=5000\left(10+20\right)$

$=5000\times 30=150000N$ .

We also know that amount of gas ejected

$\left(\frac{dm}{dt}\right)=\frac{F}{v}=\frac{150000}{800}=187.5kg/s$