Question

A rocket of initial mass $6000kg$ eject gases at a constant rate of $16kg{s}^{-1}$ with constant relative speed of $11km{s}^{-1}$. What is the acceleration of 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)

$35m{s}^{-2}$

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