Find the maximum height of a rocket fired vertically

galuda

Homework Statement

A rocket is fired vertically, ejecting sufficient mass to move upward at a constant acceleration of 2.86g. After 50.2s, the rocket motors are turned off, and the rocket subsequently moves under the action of gravity alone, with negligible air resistance. Ignoring the variation of g with altitude, find the maximum height the rocket reaches.

s = 1/2 at^2

The Attempt at a Solution

I guess during the burn i would use this formula to get .5(2.86*9.8)(50.2)^2, but i don't know where to go after that

$$2a(y-y_0)=v^2-v_0^2$$
Where $$y_0$$ is the height of the rocket when the burn stopped. And $$a=-g$$.