To begin, we know that the bullets maximum velocity is 282 m/s; and once the bullet has been fired it will not speed up due to gravity.
The equation for velocity is v = v0 - at
Where v0 is the intial velocity 282 m/s and a is the acceleration of gravity, which is about -9.8 m/s^2. The acceleration of gravity can either be positive or negative depending on the problem.
Our equation for this problem would look like this:
v = 282 - 9.8t
This is important because it enables you to determine t or the time it will take to reach the maximum height. The bullet slows down until its velocity is 0. After that the velocity becomes negative and the bullet comes back down. The point where velocity = 0 is where the maximum height occurs.
t = 282/9.8 = 28.7755 seconds
The equation to find height is also necessary to completely solve this problem. The equation to find height is :
h(t) = h0 + v0 t + .5 a t^2
Because you are starting at the ground level, h0 is 0, v0 and a are the same as before
h(t) = 282t - 4.9 t^2
Now you can plug 28.7755 into the equation to solve for the maximum height
h(28.7755) = 282(28.7755) - 4.9 (28.7755)^2 = 4,057.34 m