Question

A space shuttle while travelling at a speed of 4000 km/h with respect to the earth disconnects and ejects a module backward, weighing one sixth of the resudual part. If the shuttle ejects the disconnected module at a speed of 100 km/h with respect to the state of the shuttle before the ejection, find the final velocity of the shuttle.

Answer 1

Suppose the mass of het shuttle including the module is M. The mass of the module will be M/6. The total linear momentum before disconnection
`=M(4000 km/h)`
The velocity of the ejected module with respect to the earth =it velocilty with respect to the shutle +the velocity of the shuttle with respect to the earth
`=-100km/h+4000km/h=3900km/h`
If the fiN/Al velocity of te shuttle is V then the total fiN/Al liner momentum
`=(5M)/6V+M/6xx3900 km/h`
By the principle of conservation of linear mometum,
`M(4000 km/h)=(5M)/6V+M/6xx3900km/h`
or `V=4020km/h`