Question

A 6000 kg rocket is set for a vertical flight. If the exhaust speed is 1000 m/s, how much gas must be ejected per second to supply the thrust needed to give the rocket an initial upward acceleration of $2m/s^2$ :

• A. 90 kg/sec
• B. 72 kg/sec
• C. 18 kg/sec
• D. 9 kg/sec

Answer 1

The correct option is B 72 kg/sec

We know that $F=\frac{\delta p}{\delta t}$

$\delta p=$rate of ejection$\times \delta t\times v$
$F=$rate of ejection $\times v$.
Also , $F-mg=ma\Rightarrow F=m(g+a)$

Therefore, rate of ejection $=\frac{m(g+a)}{v}=\frac{6000\times 12}{1000}=72$kg s${}^{-1}$.