Question

A rocket of mass $5000$ kg is to be projected vertically upwards. The gases are exhausted vertically downwards with velocity $1000$ m/s with respect to the rocket. What is the minimum rate of burning the fuel so as to just lift the rocket upwards against gravitational attraction?

Answer 1

Given mass of the rocket=5000 kg and velocity of rocket $v_r$=1000 m/s.

We know rate of burning of fuel is the amount of fuel burned with respect to time and is denoted by $\frac{dm}{dt}$.

So Force required by the rocket to launch F$=v_r\frac{dm}{dt}$

Thus rate of burning of fuel $\frac{dm}{dt}$ $=\frac{\text{mass}\times \text{gravity}}{v_r}=\frac{5000\times 10}{1000}=50$ kg/s