A rocket with lift-off mass of m, is launched from groundlevel. During flight, fuel burns at a constant rate for $$\tau$$ seconds and exhaust gasesare ejecting from the bottom of the rocket at $$\beta$$ Kg/sec with speed of c m/s relative to the rocket. Ignoring air resistance and assume acceleration due to gravity, g as constant, which of the following expression represents velocity of rocket v(t).