Question

At one instant of time a rocket is traveling in outer space at 2500m/s and is exhausting fuel at a rate of 100 kg/s. If the speed of the fuel as it leaves the rocket is 1500 m/s, relative to the rocket, the thrust is:

Answer 1

Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction on that system. Mathematically can be written as,

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

Here,

v = speed of the exhaust gases measured relative to the rocket.

$\frac{dm}{dt}$= Rate of change of mass with respect to time

Our values are given as,

$v = 1500m/s$

$\frac{dm}{dt} = 100kg/s$

Replacing we have that

$T = 1500*100$

$\therefore T = 1.5*10^5N$