Question

A rocket of initial mass $6000kg$ ejects gases at a constant rate of $16kg$ $s^{-1}$ with constant relative speed of $11km$ $s^{-1}$. What is the acceleration of the rocket one minute after the blast ?

• A. $25m$ $s^{-2}$
• B. $50m$ $s^{-2}$
• C. $10m$ $s^{-2}$
• D. $35m$ $s^{-2}$

Answer 1

Answer: (D)

Acceleration of the rocket at any instant $t$ is
$a=\frac{v_r\frac{dm}{dt}}{M-t\frac{dm}{dt}}$
Here, $M=6000kg,$ $\frac{dm}{dt}$ $=16kg$ $s^{-1}$
$v_r$ $=11km$ $s^{-1}$ $=11000m$ $s^{-1},$ $t=1$ $min=60s$
$\therefore$ $a$ $=\left[\frac{11000\times 16}{6000-60\times 16}\right]$ $m{s}^{-2}$ $\approx 35m$ $s^{-2}$