A space vehicle is traveling at 4150 km/h relative to the Earth when the exhausted rocket motor (mass 4m) is disengaged and sent backward with a speed of 79 km/h relative to the command module (mass m). What is the speed of the command module relative to Earth just after the separation? km/h

4213.2 Km/h

Explanation:

Given:

Initial Speed of space vehicle relative to Earth, u = 4150 km/h

Mass of rocket motor = 4m

speed of the rocket motor relative to command module, v' = 79 Km/h

Mass of the command module = m

Now,

let the speed of command module relative to earth be 'v'

From the conservation of momentum, we have

(4m + m) * u = m * v + (4m * (v - v'))

or

5m * 4150 = mv + 4mv - 4mv'

or

20750 = 5v - (4 * 79)

or

20750 = 5v - 316

or

v = 4213.2 Km/h