Question

A $6000kg$ rocket is fired vertically. If the exhaust speed is $1000m/s$, how much gas must be ejected each second to supply the thrust needed to overcome the weight of the rocket?

• A. $22.2m/s$
• B. $37.6kg/s$
• C. $58.8kg/s$
• D. None of these

Answer 1

The correct option is C $58.8kg/s$

To overcome the weight of the rocket, we have the condition,

magnitude of thrust $=$ weight of the rocket

$u\frac{dm}{dt}=m_{0}g$

$\frac{dm}{dt}=\frac{m_{0}g}{u}=\frac{6000\times 9.8}{1000}$

$\frac{dm}{dt}=58.8kg/s$