1.

A rocket accelerates straight up by ejecting gas downwards . In small time interval Deltat , it ejects a gas of mass Deltamat a relative speed u . Calculate kE of the entire system at t+Deltat and tand show that the device that ejects gas does work = (1/2) Delta"mu"^(2) in this time interval (negative gravity ).

Answer» <html><body><p></p>Solution :M =mass of rocket at t <br/> v = velocity of rocket at t <br/> `Deltam ` = mass of ejected <a href="https://interviewquestions.tuteehub.com/tag/gas-1003521" style="font-weight:bold;" target="_blank" title="Click to know more about GAS">GAS</a> in `Deltat` <br/> u = relative <a href="https://interviewquestions.tuteehub.com/tag/speed-1221896" style="font-weight:bold;" target="_blank" title="Click to know more about SPEED">SPEED</a> of ejected gas <br/> <a href="https://interviewquestions.tuteehub.com/tag/consider-2017521" style="font-weight:bold;" target="_blank" title="Click to know more about CONSIDER">CONSIDER</a> at time t + `Deltat` <br/> `(KE)_(t) +(KE)_(Deltat) = `KE of rocket + Ke of `= 1/2 (M-Deltam) (v+Deltav)^(2) +1/2Deltam (v-u)^(2)` <br/> `1/2 Mv^(2) +Mv Deltav -Deltamvu +1/2 Delta"mu"^(2)` <br/> `(KE)_(t) =` KE of the rocket at time t = `1/2 Mv^(2)` <br/> `DeltaK - (KE)_(t) +(KE)_(Deltat) -(KE)_(t)` <br/> `(MDeltav - Delta"mu") v +1/2 Delta" mu"^(2)` <br/> Hene , `M (dv)/(dt) =(dc)/(dt) |u|` <br/> ` :. M Deltav = Delta"mu"` <br/> `:. DeltaK = 1/2 Delta"mu"^(2)` <br/> Now , by work - <a href="https://interviewquestions.tuteehub.com/tag/energy-15288" style="font-weight:bold;" target="_blank" title="Click to know more about ENERGY">ENERGY</a> theorem , <br/> `DeltaK = Delta W ` <br/> ` :. Delta W = 1/2 Delta"mu"^(2)`</body></html>


Discussion

No Comment Found

Related InterviewSolutions