Question

A student is trying to optimize the exhaust shape of a rocket. They designed a new shape, and are trying to figure out how fast it allows the burning fuel to flow out of the rocket. The student takes a rockets that weighs 10.43 kg empty and loads 8.79 kg of fuel. The student aims the rocket horizontally, lights it, and watches it take off. The rocket exhausts the fuel before dropping to the ground. Right before the fuel is exhausted, the student - equipped with a speedometer - observes the velocity x-component of the rocket is 29.373 m/s. Assuming no air drag, perfect rocket efficiency, and constant mass flow, what was the speed of the ejected fuel relative to the rocket? Include units in SI

Answer 1

-- (1)

Here ,

v = velocity of rocket at any given time

mi = Total initial mass of the rocket (mass of rocket + mass of fuel)

m = mass of the rocket at any given time

vi = initial velocity of the rocket

u = relative velocity of fuel with respect to the rocket

Since, here vi = 0 as the initial the rocket is starting from rest, equation (1) becomes,

When v=29.373, all the fuel has been exhausted thus mass of rocket m = 10.43 kg

substituting values,