Rocket question. (1 Viewer)

[Ioup]

Can someone help with this question please.

A rocket has a mass of 8*10e6 kg of which 75% is fuel. Its engines burn fuel at 2.5kg*10e5 kg min-1. The rocket has an initial acceleration of 4ms-2 up.
a) Calculate the thrust the engines develop.
b) Calculate how much fuel remains after 3 minutes.
c) Calculate the total time the rockets will fire.
d) Calculate the acceleration of the rocket after 2 minutes.

 

[zeropoint]

Can someone help with this question please.

A rocket has a mass of 8*10e6 kg of which 75% is fuel. Its engines burn fuel at 2.5kg*10e5 kg min-1. The rocket has an initial acceleration of 4ms-2 up.
a) Calculate the thrust the engines develop.
b) Calculate how much fuel remains after 3 minutes.
c) Calculate the total time the rockets will fire.
d) Calculate the acceleration of the rocket after 2 minutes.

a)
The thrust T is related to the mass flow rate mdot and the exhaust velocity Ve by the relationship

T = mdot * Ve

b)

The mass at time time t = 0 is m(0) = 0.75 * 8*10e6 kg. In an interval of time of time Δt the mass lost to exhaust is Δm = mdot * Δt, so after Δt = 3 min the mass of fuel remaining is

m(3 min) = m(0) - mdot * Δt

c)

The rockets will fire until the mass of the fuel is zero

m(t) = m(0) - mdot * t --- (*)

Put m(t) = 0 and you get t = m(0) / mdot.

d)

Calculate the mass of the fuel after 2 min using Eq. (*), and then add this to the mass of the rocket body to get the total mass M after 2 min. Apply Newton's second law

+ M a = - M g + T

and divide by M to get the acceleration a, assuming that the gravitational acceleration remains approximately constant.

James