Question

A space vehicle is traveling at 4300 ????m/ℎ relative to Earth when the exhausted rocket motor (mass 4m) is disengaged and sent backward with a speed of 82 ????m/ℎ relative to the command module (mass m). What is the speed of the command module relative to Earth just after the separation?

Answer 1

4361.5 km/h

Step-by-step explanation:

v = Velocity of space vehicle = 4300 km/h

`v_1` = Velocity of exhaust

`v_2` = Velocity of module

Relative velocity

`v_r=v_2-v_1=82\\\Rightarrow v_1=v_2-82`

4m = Mass of rocket

m = Mass of module

3m = Mass of rocket without module

In this system linear momentum is conserved

`4mv=3mv_1+mv_2\\\Rightarrow 4v=3(v_2-82)+v_2\\\Rightarrow 4* 4300=3v_2-246+v_2\\\Rightarrow 17446=4v_2\\\Rightarrow v_2=(17446)/(4)\\\Rightarrow v_2=4361.5\ km/h`

The speed of the command module relative to Earth just after the separation is 4361.5 km/h