Question

A space vehicle is traveling at 4060 km/ hrelative to Earth when the exhausted rocket motor is disengaged and sent backward. relative speed between the motor and the command module is then 80 km/h. The mass of the motor is four times the mass of th module. What is the speed of the command module relative to Earth just after the separation?

Answer 1

The speed of the command module relative to Earth just after the separation is approximately 748 km/h.

Step-by-step explanation:

To find the speed of the command module relative to Earth just after the separation, we can use the principle of conservation of momentum.

Let's assume the mass of the module is 'm' and the mass of the motor is '4m'.

According to the conservation of momentum, the total momentum before separation is equal to the total momentum after separation.

Before separation, the momentum of the module is (mass of the module x speed of the module relative to Earth) and the momentum of the motor is (mass of the motor x speed of the motor relative to Earth).

After separation, the momentum of the module is (mass of the module x speed of the module relative to Earth just after separation) and the momentum of the motor is (mass of the motor x speed of the motor relative to Earth just after separation).

Since the total momentum before separation is equal to the total momentum after separation, we can write the equation:

(m x 4060 km/h) + (4m x (-80 km/h)) = (m x v) + (4m x (-v))

Here, 'v' is the speed of the command module relative to Earth just after the separation.

Simplifying the equation:

4060m - 320m = 5mv

3740m = 5mv

Dividing both sides by '5m', we get:

v = 3740/5 km/h

v ≈ 748 km/h

Therefore, the speed of the command module relative to Earth just after the separation is approximately 748 km/h.