Consider a rocket which has two combustion rates, ? 1 = 4 kg / s and ? 2 = 8 kg

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

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