Question

The lunar model ascent vehicle was a rocket that lifted off from the surface of the Moon. The Moon's mass and radius are, respectively M = 7.33 x 1022 kg, and Rm = 1.73 x 106m. The rocket expelled exhaust gases at Ve = 3.0 x 103 m/s. Its initial mass, including fuel, was 4800 kg, and it burned fuel at a rate Am/At= 10 kg/s. Calculate the initial acceleration of the rocket taking off from the surface of the Moon. 6.25 m/s2 4.62 m/s2 5.13 m/s2 1.63 m/s2

Answer 1

Here,

at the surface of moon

g =G * M/r^2

g = 6.673 *10^-11 * 7.33 *10^22/(1.73 *10^6)^2

g = 1.63 m/s^2

let the acceleration is a

dm/dt = 10 Kg/s

Ve = 3 *10^3 m/s

using second law of motion

dm/dt * Ve - m *g = m * a

10 * 3 *10^3- 4800 * 1.63 = 4800 * a

a = 4.62 m/s^2

initial acceleration of the rocket is 4.62 m/s^2