Question

A rocket, with an initial mass of 1000 kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 10 kg per second. The burnt matter is ejected vertically downwards with a speed of $2000m/s$ relative to the rocket. Find the velocity of the rocket after 1 min of start.

• A. 1232.6
• B. 13.6
• C. 13
• D. 132.6

Answer 1

The correct option is A 1232.6

$\text{Given}:$ u=0, t=60s, g=10 $m/s^2$, $v_r=2000m/s$, $m_0$=1000kg and $m=1000-10\times 60=400kg$

$\text{Solution}:$

The velocity equation is given by

$v=u-gt+v_{r}In\frac{m_0}{m}$

Putting the given values we get

$v=0-600+2000In\frac{1000}{400}$= $2000In2.5-600=1232.6m/s$

$\text{Hence A is the correct option}$