s=ut-gt^2/2 is the equation of motion where g=9.81 m/s/s is the approximate acceleration of gravity and u=initial speed=300m/s.
This is the equation of a parabola and the maximum height is the vertex. At this point the vertical speed is zero as the bullet slows down under gravity and then reverses direction. The rate of change of the height is the speed and this is u-gt. When this is zero u=gt so t=u/g=300/9.81=30.58 m/s. s=300*300/9.81-9.81*(300/9.81)^2/2=4587.2m approx. So the max height is about 4587m, and the time to reach that height is about 30.6 seconds.
When s=200, 200=300t-gt^2/2 so t^2-600t/g+400/g=0 from which t^2-600t/g+(300/g)^2=(300/g)^2-400/g; (t-300/g)^2=(300/g)^2-400/g. t-300/g=±√((300/g)^2-400/g)=±29.91 approx. Therefore t=300/g±29.91, t=60.49 seconds (downward path). The speed is 300-gt=-293.41m/s which means (because of the minus sign) that the bullet is travelling down at a speed of 293.41 m/s (approx).