[UPSC CSE 1986] Conservation Laws (Q61, 20M)

A rocket is fired vertically up. During the burning of the engine, which lasts for 50\text{ s}, a constant acceleration of 2.0\text{ g} is observed. What is the speed of the rocket at the end of 50\text{ s}? Calculate the maximum height to which the rocket will rise before it begins to fall back. Take = g = 9.80\text{ ms}^{-2} and neglect the variation of g with height.