In order to find the maximum height, we need to find the vertex of the quadratic equation.
To do so, first let's identify the parameters a, b and c from the standard form:
[tex]\begin{gathered} y=ax^2+bx+c \\ h=-5t^2+60t+0 \\ a=-5,b=60,c=0 \end{gathered}[/tex]Now, we can use the formula below for the vertex x-coordinate:
[tex]t_v_{}=\frac{-b}{2a}=\frac{-60}{-10}=6[/tex]Now, calculating the vertex y-coordinate, we have:
[tex]\begin{gathered} h_v=-5t^2_v+60t_v \\ h_v=-5\cdot6^2+60\cdot6 \\ h_v=-180+360 \\ h_v=180\text{ meters} \end{gathered}[/tex]Therefore the maximum height is 180 meters.
Since the vertex occurs for a time of 6 seconds and the time of flight is double the vertex time, the flight time is 12 seconds.
