Question

A rocket of mass $20kg$ has $180kg$ of fuel. The exhaust velocity of the fuel is $1.6km/sec$. Calculate the minimum rate of consumption of fuel so that the rocket may rise from the ground. Also calculate the ultimate vertical speed gained by the rocket when the rate of consumption of fuel is $2kg/sec$.

Answer 1

Velocity of rocket is given as

$v=uln\frac{M}{M-rt}$

where $M$ is the Total mass of rocket and fuel at $t=0$ second

That is,

$M=20+180=200kg$

and

Rate of consumption of fuel, $r=2kg/sec$

Velocity of gas rejection with respect to rocket, $u=1.6km/sec$

Ultimate velocity is achieved when all the fuel burns,

That is,

$M-rt=20kg$

So,

$v=1.6ln\frac{180}{20}=3.515km/sec$