Question

The exhaust velocity of the gases coming out of a rocket is $350\text{m/s}$ w.r.t the rocket. The rocket can burn fuel at a rate of $80\text{kg/s}$. For a successful launch, the desired acceleration of the rocket is $4{\text{m/s}}^2$. What is the initial total mass of this rocket? (Take $g=10{\text{m/s}}^2$)

• A. $3000\text{kg}$
• B. $2000\text{kg}$
• C. $1500\text{kg}$
• D. $2500\text{kg}$

Answer 1

The correct option is B $2000\text{kg}$

Relative velocity of exhaust gases $v_r=350\text{m/s}$
Rate of combustion of fuel $=\frac{dM}{dt}=80\text{kg/s}$
Required acceleration of the rocket $a=4{\text{m/s}}^2$
We have the equation,
$v_r\frac{dM}{dt}-Mg=Ma$
$\Rightarrow 350\times 80=M(g+a)$
$\Rightarrow 28000=M(10+4)$
$\Rightarrow M=2000\text{kg}$
Hence the initial total mass of the rocket is $2000\text{kg}$.