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A space vehicle is traveling at 4750 km/h relative to the Earth when the exhausted rocket...

A space vehicle is traveling at 4750 km/h relative to the Earth when the exhausted rocket motor (mass 4m) is disengaged and sent backward with a speed of 81 km/h relative to the command module (mass m). What is the speed of the command module relative to Earth just after the separation? km/h

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Answer #1
 

Then according to the law of conservation of linear momentum

MU = (M-m)V + mv

Also we are given that M= 5, m=4 , (M-m)=1 , U= 4750km/h, (V-v)= 81km/h. then the equation becomes

(5*4750) = V + 4(V-81)

then V= 4764.8

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