Question

A rocket with an initial mass of $1000\text{kg}$ is launched vertically upwards from rest, under gravity. The rocket burns fuel at the rate of $10\text{kg/sec}$. The burnt matter is ejected vertically downwards with speed of $2000{\text{ms}}^{-1}$ relative to rocket. If the burning stops after one minute, find the maximum velocity of the rocket.
[Take $g=10{\text{m/s}}^2,\ln \left(2.5\right)=0.92$]

• A. $1442{\text{ms}}^{-1}$
• B. $1240{\text{ms}}^{-1}$
• C. $1032{\text{ms}}^{-1}$
• D. $836{\text{ms}}^{-1}$

Answer 1

The correct option is B $1240{\text{ms}}^{-1}$

As we know, the rocket takes off due to the mass ejected from the rocket which gives thrust to it.
Maximum velocity attained is,
$v_{max}=u-gt+v_r\ln \left(\frac{m_0}{m}\right)$

Here,
$u=0,t=60\text{s},v_r=2000{\text{ms}}^{-1}{m}_0=1000\text{kg},m=(1000-10\times 60)=400\text{kg}$
Putting the values in the equation, we get
$v_{max}=0-(10\times 60)+2000\ln \left(\frac{1000}{400}\right)=1240{\text{ms}}^{-1}$

Hence, $\left(B\right)$ is the correct answer.