Given relation between height and time is:
[tex]h=175t-16t^2[/tex]Now put the value of h=85 ft in given relation:
[tex]85=175t-16t^2[/tex]Solving it for t:
[tex]\begin{gathered} 16t^2-175t-85=0 \\ t=\frac{175\pm\sqrt[]{(-175)^2-4\times16\times85}}{2\times16} \\ t=\frac{175\pm\sqrt[]{30625-5440}}{32} \\ t=\frac{175\pm\sqrt[]{25185}}{32} \\ t=\frac{175\pm158.6}{32} \\ t=0.51\text{ or }10.43\text{ second} \end{gathered}[/tex]