Consider a rocket which has two combustion rates, ? 1 = 4 kg / s and ? 2 = 8 kg
ID: 2144720 • Letter: C
Question
Consider a rocket which has two combustion rates, ?1= 4kg/sand ?2= 8kg/s. The relative speed of the exhaust gas is 90 m/s in either case.
The rocket starts from rest, in empty space. The initial mass ism0= 4000kg, of which 3000 kg is fuel. For timetfrom 0 to 250 s, the rocket runs at combustion rate ?1. Then for timetfrom 250 s to 500 s, the rocket runs with combustion rate ?2.
(A) Determine the final speed of the rocket.
(B) Plot an accurate graph of velocity as a function of time.
PLEASE show solutions and explain.
Explanation / Answer
thrust produced = 4 x 90
4 x 90 = (4000 - 4t) xa (from 0 to 250 s)
as a = dv/dt
dv = 90 / (1000 - t) dt
integrating this from 0 to 250
v = -90 ln(1000 - t) (0 to 250)
= 25.9 m/s
now the mass of the rocket is reduced to 3000
8 x 90 = (3000 - 8t)xa now we should consider time from 0 as we already reduced the mass
doing the same as above
v - 25.9 = -4 x90/8ln(3000 - 8t) (0 to 250)
V = 75.33m/s