Question

A $7500kg$ rocket is set for vertical firing. The exhaust speed is $800m/s$ w.r.t. rocket. To give an vertical upward acceleration of $10m/s^2$, the amount of gas ejected per second for the needed thrust will be

• A. $127.5kg/s$
• B. $137.5kg/s$
• C. $185.5kg/s$
• D. $187.5kg/s$

Answer 1

The correct option is D $187.5kg/s$

Given,

$m=7500$kg, $v=800$m/s

$a=10$ $m/l^2$,

we know,

Thrust$=v\frac{dm}{dt}$;

$v=$exhaust speed

$m=$amount of gas ejected

The upward force can also be found as,

$F=m(a+g)$;

$a=$acceleration of rocket

$g=$acceleration due to gravity

$=9.8m/s^2$

$\therefore$ Thrust $=F$

$v\frac{dm}{dt}=m(a+g)$ .........$\left(1\right)$

Substituting the given values in equation $\left(1\right)$, we get

$800\times \frac{dm}{dt}=7500\times (10+9.8)$

$\Rightarrow \frac{dm}{dt}=185.625$kg/s

But, if we take $g=10$m/s

We get $\frac{dm}{dt}=187.5$ kg/s

$\therefore$ The amount of gas ejected for providing thrust

$\frac{dm}{dt}=187.5$ kg/s.