Question

A $1000kg$ rocket is fired from the ground so that exhaust speed is $400m/s$. If rocket accelerates with $5m{s}^{-2}$ initially then fuel burning rate is

• A. $25kg/s$
• B. $30kg/s$
• C. $37.5kg/s$
• D. $50kg/s$

Answer 1

The correct option is C $37.5kg/s$

Given, Mass of the rocket $=100kg$

speed $u=400m/s$

Acceleration $a=5m/s^2$

So, the rate of burning $=\frac{dm}{dt}$

Thrust on the rocket $F=u\left(\frac{dm}{dt}\right).........1$

Using Newton's law $ma=u\frac{dm}{dt}-mg$

$\left(1000\right)5=\left(400\right)\frac{dm}{dt}-1000\times 10$

$\Rightarrow \frac{dm}{dt}=37.5kg/s$