we have the quadratic equation
![h=175t-16t^2](https://img.qammunity.org/2023/formulas/mathematics/college/718ggl2e5w09hthn0mk8ffuy5qiz7xubbt.png)
For h=85 ft
substitute in the given equation
![\begin{gathered} 85=175t-16t^2 \\ 16t^2-175t+85=0 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/zeln3m9dglsli7pthwncodkxwh9j7zgnhz.png)
Solve the quadratic equation
Using the formula
a=16
b=-175
c=85
substitute
![t=(-(-175)\pm√(-175^2-4(16)(85)))/(2(16))](https://img.qammunity.org/2023/formulas/mathematics/college/ac4cn4blvjmezygh2smbm5eif5b90o439x.png)
![t=(175\pm158.70)/(32)](https://img.qammunity.org/2023/formulas/mathematics/college/wn1adnv7pjmpz91sglnpehfpsuphvp6tth.png)
the values of t are
t=10.43 sec and t=0.51 sec
Verify with the graph
using a graphing tool
is ok
the answer is
t=0.51 sec and t=10.43 sec