Question

A Saturn-V Rocket has a total mass of 3.00 times 10^6 kg when fully fueled. The first stage of rocket propulsion burns 2.27 times 10^6 kg of fuel in 150 s, providing a thrust of 3.402 times 10^7 N, as the rocket is lifted against Earth's gravity. a) Find the rate at which fuel is burned during this first-stage propulsion, assuming a steady rate of fuel consumption. b) Find the exhaust speed of the fuel as it is ejected from the rocket. c) Find the acceleration of the rocket when the rocket first starts to burn. d) Find the acceleration of the rocket immediately before the fuel is exhausted.

Answer 1

a) rate of burning=( 2.27 x 10^6) kg/ 150 sec = 1.5133 x 10^ 5 kg/sec

b) V+Ve ( exhaust speed of fuel with respect to rocket) = 3.402 x 10^7 ( 1/ 1.5133 x 10^ 5) = 2.24806 x 10^2 m/sec

c) a= ( 2.24806 x 10^2 )( 1.5133 x 10^ 5 kg/sec)/ 3 x 10^6 -9.8

a=1.54 m/s^2

d)let's calculate the final velocity ( the time at which the entire fuel is burned)'

v= 2.24806 x 10^2 ln (3 x1 0^6/ 0,.73 x 10^6) = 2.24806 x 10^2 x 1.413 = 3.178 x 10^2 m/s

a= 3.178 x 10^2/ 150= 2.11 m/s^2