A solid motor has an average thrust of 67,000 N, a specific impulse of 285 sec, and a propellant mass fraction of 0.92. Calculate the total mass of the vehicle for a 42 sec burn time.

total mass is 1095.096 kg

Explanation:

given data

thrust = 67000 N

impulse time t = 285 sec

mass fraction = 0.92

to find out

total mass of the vehicle

solution

we know here thrust formula that is

thrust = m * g * t

put here value and find m

m = 67000 / 9.8 (285)

m = 23.988 kg/s

so here mass fraction is express as

mass fraction = m * time / (m * time + mf)

put here time after 42 sec

0.92 = 23.988 * 42 / (23.988 * 42 + mf)

(23.988 * 42 + mf) 0.92 = 23.988 * 42

mf = 87.60 kg

total mass = mf + m * time

put here value

total mass = 87.60 + 23.988 * 42

total mass is 1095.096 kg