Question

A rocket with an initial mass $m=2000\text{kg}$ is launched vertically upwards. The rocket burns fuel at the rate of $20\text{kg/s}$. The burnt material is ejected vertically downwards with a speed of $4000\text{m/s}$ relative to the rocket. If burning stops after $30$ seconds, find the maximum velocity of the rocket. (Take $g=10{\text{m/s}}^2$ )

• A. $0\text{m/s}$
• B. $4515.9\text{m/s}$
• C. $1126.7\text{m/s}$
• D. $300\text{m/s}$

Answer 1

The correct option is C $1126.7\text{m/s}$

Given,
Initial mass of Rocket $m_0=2000\text{kg}$
Rocket fuel burning rate $\mu =20\text{kg/s}$
Burnt matter ejection speed $v_r=4000\text{m/s}$
From velocity equation $v=u-gt+v_r\ln \left(\frac{m_o}{m}\right)$
Here $u=0$, initially. At $t=30\text{sec}$,
$v=0-10\times 30+4000\times \ln \left(\frac{2000}{2000-20\times 30}\right)$
$(\because m=m_0-\mu t)$
$v=1126.7\text{m/s}$