Answer:
The person on the Ferris wheel will be 63 ft above the ground at;
[tex]\begin{gathered} t=9.03\text{ seonds} \\ \text{and} \\ t=22.98\text{ seconds} \end{gathered}[/tex]Explanation:
Given that the height of the function can be modeled using the function;
[tex]h(t)=53+50\sin (\frac{\pi}{16}t-\frac{\pi}{2})[/tex]For the person to be 63 ft above the ground;
[tex]\begin{gathered} h(t)=63=53+50\sin (\frac{\pi}{16}t-\frac{\pi}{2}) \\ 63=53+50\sin (\frac{\pi}{16}t-\frac{\pi}{2}) \\ 63-53=50\sin (\frac{\pi}{16}t-\frac{\pi}{2}) \\ \frac{10}{50}=\sin (\frac{\pi}{16}t-\frac{\pi}{2}) \end{gathered}[/tex]solving further;
[tex]\begin{gathered} \frac{10}{50}=\sin (\frac{\pi}{16}t-\frac{\pi}{2}) \\ \sin ^{-1}(\frac{10}{50})=(\frac{\pi}{16}t-\frac{\pi}{2}) \\ 0.201=(\frac{\pi}{16}t-\frac{\pi}{2}) \\ \frac{\pi}{16}t=\frac{\pi}{2}+0.201 \\ t=\frac{\frac{\pi}{2}+0.201}{\frac{\pi}{16}} \\ t=9.03\text{ seonds} \\ or \\ (\pi-0.201)=(\frac{\pi}{16}t-\frac{\pi}{2}) \\ \frac{\pi}{16}t=\frac{\pi}{2}+(\pi-0.201) \\ t=\frac{\frac{\pi}{2}+(\pi-0.201)}{\frac{\pi}{16}} \\ t=22.98\text{ seconds} \end{gathered}[/tex]Therefore, the person on the Ferris wheel will be 63 ft above the ground at;
[tex]\begin{gathered} t=9.03\text{ seonds} \\ \text{and} \\ t=22.98\text{ seconds} \end{gathered}[/tex]