Question

12. The only rocket that has ever lifted humans beyond low Earth orbit was the Saturn V, which had three stages of propulsion. Fully fueled, the rocket plus its cargo had a mass of 2.97x10 kg. The first stage consumed fueltoxidizer at a rate of 1.5x10 kgs, and had an exhaust speed of 2.6x10*m/s. (a) Calculate the thrust that was produced by the first stage. (b) Determine the acceleration of the rocket just after lift-off from the launch pad. 3

Answer 1

Given,

M = 2.97 x 10^6 kg ; dm/dt = 1.5 x 10^4 kg/s ; v = 2.6 x 10^3 m/s

a)We know that

T = dm/dt x v

T = 1.5 x 10^4 x 2.6 x 10^3 = 3.9 x 10^7 kg- m/s^2

Hence, T = 3.9 x 10^7 kg-m/s^2 or N

b)T = M a=> a = T/M

a = 3.9 x 10^7/2.97 x 10^6 = 13.13 m/s^2

Hence, a = 13.13 m/s^2