Aspace vehicle is traveling at 5000 km/h relative to the earth when the exhausted rocket motor is disengaged and sent backward with a speed of 71 km/h relative to the command module. the mass of the motor is four times the mass of the module. what is the speed of the command module relative to earth just after the separation?

The speed of the command module relative to earth just after the separation is 4985.8 km/h

Explanation:

Given that,

Velocity of vehicle = 5000 km/h

Relative velocity = 71 km/h

The mass of the motor is four times the mass of the module.

We need to calculate the velocity of motor

Using formula of relative velocity

Put the value into the formula

We need to calculate the speed of the  command module relative to Earth just after the separation

Using conservation of momentum

Put the value into the formula

Hence, The speed of the command module relative to earth just after the separation is 4985.8 km/h

0.19 m/s and 0.45 m/s