When calculating the speed of the command module after the separation of the exhausted rocket motor, we can apply the principle of conservation of momentum. This principle states that the total momentum of a system remains constant if no external forces are acting on it.
First, let's calculate the initial momentum of the system before separation. The momentum of an object is calculated by multiplying its mass by its velocity. The mass of the command module is denoted by M, and the mass of the rocket motor is four times the mass of the module, so the mass of the rocket motor is 4M.
The initial momentum of the system is given by:
Initial momentum = (mass of command module x velocity of command module) + (mass of rocket motor x velocity of rocket motor)
Given that the speed of the command module is 3860 km/h and the speed of the rocket motor is 125 km/h, we convert these speeds to the same unit for calculation.
Now, the initial momentum of the system is:
Initial momentum = (M x 3860) + (4M x (-125))
After separation, the total momentum of the system remains constant. Let V be the final velocity of the command module after separation. The final momentum of the system is:
Final momentum = (M x V) + (4M x 0)
Using the conservation of momentum principle, we can equate the initial momentum to the final momentum:
(M x 3860) + (4M x (-125)) = (M x V)
Now, solve for V to find the speed of the command module after the separation.
