Question

A rocket has total mass Mi=360 kg , including Mf=330kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x=0 , turns on its engine at time t=0 , and puts out exhaust with relative speed ve=1500 m/s at the constant rate k=2.50 kg/s . The fuel will last for a burn time of Tb = Mf / k = 330 kg /(2.5kg /s)=132s . (a) Show that during the burn the velocity of the rocket as a function of time is given byv(t)=-ve (1- kt / Mi)

Answer 1

let the parameters are:

M=instantaneous mass of the rocket

v=velocity of the rocket

t=time

initial mass=Mi=360 kg

fuel mass=Mf=330 kg

relative speed=Ve=1500 m/s

rate of mass decay=k=2.5 kg/s

writing newton’s second law of motion:

                    M*du/dt=-Ve*dM/dt

                           ==>du=-Ve*dM/M

Integration of both sides,

                       u=-Ve*ln(M)

using the limits with at t=0, u=0 and velocity being v(t),

at t=0, mass=Mi, at any time t, mass=Mi-k*t

                 v(t)-0=-Ve*ln((Mi-k*t)/Mi)

                  v(t)=-Ve*ln(1-(k*t/Mi))

What is needed for rocket propulsion?

Rocket propulsion is the strategy utilized to make the basic thrust to lift a rocket into the air. The force that the rocket employments to lift off from the soil is known as rocket propulsion. The third law of movement by Newton serves as the foundation for rocket propulsion. Here, the fuel is shot out from the exit mightily in arrange to cause an equal and converse reaction. The some sorts of rocket propulsion are fuelled by liquid, strong, cold gas, and particles. The rocket's mass, fuel burn rate, and weaken speed all impact speeding up.

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