A rocket is moving with constant acceleration 6. 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 6. Assume external force

1.	A rocket is moving with constant acceleration 6. 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 ) `:. M omega = -u (dM)/(dt)` ( where ` omega` is its acceleration ) `(dM)/(M) =(-d omega)/( u)` Integrating LOG `M=-(omega)/(u)t+C` when t=0, `M=M_0` so ` C= log M_0 , log M = -(omega)/(u) t + log M_0 :. log (M)/(M_0) = -(omega)/(u) t` ` (M)/(M_0)=e^((omega)/(u)t) or M = M_0e^((omega)/(u)t)` Thus , the MASS of the rocket changes exponentially