A rocket is moving with constant acceleration omega . Assume external forces on it to be zero . Exhaust gases escape with velocity u relative to the rocket . Find how its mass changes with time if its initial mass is m_(0).

A rocket is moving with constant acceleration omega . Assume external

1.	A rocket is moving with constant acceleration omega . Assume external forces on it to be zero . Exhaust gases escape with velocity u relative to the rocket . Find how its mass changes with time if its initial mass is m_(0).
Answer» Solution :`F=d/(dt) (-Mu)--U(DM)/(dt)` (since u is constant) `:. Momega =-u(dM)/(dt)` ( where `omega` is its acceleration ) `(dM)/M =(-domega)/u` Integrating `log M =-omega/ut+C` when `t=0, M=M_(0)` so `C=log M_(0), log M=-omega/ut+log M_(0) :. log M/M_(0)= - omega/ut` `M/M_(0)=E^(-omega/ut) "or" M= M_(0)e^(-omega/ut)` THUS , the MASS of the rocket changes exponentially