Question

A space vehicle is traveling at 5125 km/h relative to the Earth when the exhausted rocket motor (mass 4m) is disengaged and sent backward with a speed of 87 km/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

1094.6 km/h

Step-by-step explanation:

`v_2` = Speed of command module

`v_1` = Speed of motor

m = Mass of motor

4m = Mass of module

v = Velocity of space vehicle = 5125 km/h

Relative velocity

`v_2-v_1=87\ km/h\\\Rightarrow v_1=v_2-87`

As the linear momentum of the system is conserved

`(m+4m)v=4mv_1+mv_2\\\Rightarrow 5mv=4mv_1+mv_2\\\Rightarrow 5v=4v_1+v_2\\\Rightarrow 5* 5125=4(v_2-87)+v_2\\\Rightarrow 5125=5v_2-348\\\Rightarrow v_2=1094.6\ km/h`

The speed of the command module relative to Earth just after the separation is 1094.6 km/h