Question

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

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

Answer 1

Answer: (D)

Acceleration of the rocket at any instant $t$ is
$a =\frac{v_{r} \frac{d \,m}{d \,t}} {M-t\frac{d\,m}{d \,t}}$
Here, $M=6000 \, kg,$ $\frac{d\, m}{d \,t}$ $=16 \, kg $ $s^{-1}$
$v_{r}$ $=11 \,km$ $s^{-1}$ $=11000 \,m$ $s^{-1},$ $t=1$ $min =60\, s$
$\therefore \quad$ $a$ $=\left[\frac{11000\times16}{6000-60\times16}\right]$ $m s^{-2}$ $\approx35 \,m$ $s^{-2}$