Question

A $5000kg$ rocket is set for vertical firing. The exhaust speed is $800m{s}^{-1}.$ To give an upward acceleration of $20m{s}^{-2},$ the amount of gas ejected per second to supply the needed thrust is $(g=10m{s}^{-2})$

• A. $127.5kg{s}^{-1}$
• B. $137.5kg{s}^{-1}$
• C. $187.5kg{s}^{-1}$
• D. $185.5kg{s}^{-1}$

Answer 1

Answer: (C)

$187.5kg{s}^{-1}$

Given that,

Mass of rocket $m=5000Kg$

Acceleration $a=20m/s^2$

Speed $v=800m/s$

$g=10m/s^2$

Now, thrust force on the rocket

$F_t=v_r\left(\frac{-dm}{dt}\right)$

Net force on the rocket

$F_{net}=F_t-W$

$ma=v_r\left(\frac{-dm}{dt}\right)-mg$

$\left(\frac{-dm}{dt}\right)=\frac{m(g+a)}{v_r}$

Rate of gas ejected per second

$\left(\frac{-dm}{dt}\right)=\frac{5000(10+20)}{800}$

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

Hence, the amount of gas ejected per second is $187.5kg/s$