Help with acceleration and thrust?

Question

A space launch vehicle has a total mass of 3,400,000 kg at lift off. The first stage contains 2,000,000 kg of propellent (fuel and oxygen) which is consumed at a rate of 14,000 kg/s.

a) What is the minimum thrust of the engines at lift off?

b) If this thrust is sustained, find the time over which the first stage operates and acceleration of the vehicle at that time. (Don't include air friction and that entire flight is vertical)

c) Find the speed of the exhaust gases.

Help plz would be much appreciated!

Answer 1

Hey! this isn't rocket science! oh wait. yes it is.

a) The force of the thrust must at least be greater than the weight
of the space launch vehicle.
Fthrust = Fweight = mg = 3400000*9.8 = 3.33E7 N

b) The fuel will be consumed in
2000000/14000 = 142.9 seconds
F = ma
Force of thrust is maintained, but the mass of the vehicle is less because the fuel is gone.
Net force = Fthrust - Fgravity = ma
3.33E7 - 1400000*9.8= (1400000)a
a = 14.0 m/s²

c) I don't think there's enough information to answer this.. you would need time to find speed. Not too sure though.

Answer 2

g = 9.80665 m·s^-2

a)
F(min) > (9.80665 m·s^-2)(3,400,000 kg
F(min) > 33,342,610 N

b) Constant thrust requires constant dm/dt, so
(2,000,000)/14,000 = 142.857 seconds
a = (T - mg)/m
Just prior to engine cutoff,
a = (33,342,610 - 2,000,000*9.0665)/2,000,000
a = 7.6 m/s^2

c)
Ve > (33342610 kgm/s^2)/(14,000 kg/s)
Ve > 2,381.615 m/s