Question

A rocket with a mass of 2.0 Ã 106 kg is designed to take off from the surface of the earth by burning fuel and ejecting it with an exhaust speed of 3500 m/s. what is the minimum rate at which the fuel should be consumed in order to attain liftoff?

Answer 1

thrust force getting from the burning of mass should balance the weight of the rocket

here thrust force is given as

$F_t = v\frac{dm}{dt}$

now by force balance we can say

$mg = v \frac{dm}{dt}$

now plug in all values in this

$(2 \times 10^6)(9.8) = 3500 \times \frac{dm}{dt}$

$\frac{dm}{dt} = \frac{19.6 \times 10^6}{3500}$

$\frac{dm}{dt} = 5600 kg/s$

so rate of mass burning per second will be 5600 kg per second in order to lift up the rocket