Question

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

• A. $127.5\, kgs ^{-1}$
• B. $137.5\, kgs ^{-1}$
• C. $185.5\, kgs ^{-1}$
• D. $187.5\, kgs ^{-1}$

Answer 1

Answer: (D)

Given : Mass of rocket $( m )=5000\, Kg$
Exhaust speed $( v )=800\, m / s$
Acceleration of rocket $(a)=20\, m / s ^{2}$
Gravitational acceleration $( g )=10\, m / s ^{2}$
We know that upward force
$F = m ( g + a )=5000(10+20)$
$=5000 \times 30=150000\, N .$
We also know that amount of gas ejected
$\left(\frac{d m}{d t}\right)=\frac{F}{V}=\frac{150000}{800}$ $=187.5\, kg / s$