A space vehicle is traveling at 2980 km/h relative to Earth when the exhausted rocket motor is disengaged and sent backward. The relative speed between the motor and the command module is then 94 km/h. 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

Question

Physics

Gabriel Downs

17 May, 10:35

A space vehicle is traveling at 2980 km/h relative to Earth when the exhausted rocket motor is disengaged and sent backward. The relative speed between the motor and the command module is then 94 km/h. 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

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Answers (1)

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Lilia Shaw · Answer 1

3054.4 km/h

Explanation:

Using the conservation of momentum

momentum before separation = 5M * 2980 Km/h where M represent the mass of the module while 4 M represent the mass of the motor

initial momentum = 14900 M km/h

let v be the new speed of the motor so that the

new momentum = 4Mv and the new momentum of the module = M (v + 94 km/h)

total momentum = 4Mv + Mv + 93 M = 5 Mv + 93M

initial momentum = final momentum

14900 M km/h = 5 Mv + 93M

14900 km/h = 5v + 93

14900 - 93 = 5v

v = 2961.4 km/h

the speed of the module = 2961.4 + 93 = 3054.4 km/h