Question

How do I solve for the ferris wheel problem? Also pi/6 should be 180/6

Answer 1

The person on the Ferris wheel will be 63 ft above the ground at;

`\begin{gathered} t=9.03\text{ seonds} \\ \text{and} \\ t=22.98\text{ seconds} \end{gathered}`

Step-by-step explanation:

Given that the height of the function can be modeled using the function;

`h(t)=53+50\sin ((\pi)/(16)t-(\pi)/(2))`

For the person to be 63 ft above the ground;

`\begin{gathered} h(t)=63=53+50\sin ((\pi)/(16)t-(\pi)/(2)) \\ 63=53+50\sin ((\pi)/(16)t-(\pi)/(2)) \\ 63-53=50\sin ((\pi)/(16)t-(\pi)/(2)) \\ (10)/(50)=\sin ((\pi)/(16)t-(\pi)/(2)) \end{gathered}`

solving further;

`\begin{gathered} (10)/(50)=\sin ((\pi)/(16)t-(\pi)/(2)) \\ \sin ^(-1)((10)/(50))=((\pi)/(16)t-(\pi)/(2)) \\ 0.201=((\pi)/(16)t-(\pi)/(2)) \\ (\pi)/(16)t=(\pi)/(2)+0.201 \\ t=((\pi)/(2)+0.201)/((\pi)/(16)) \\ t=9.03\text{ seonds} \\ or \\ (\pi-0.201)=((\pi)/(16)t-(\pi)/(2)) \\ (\pi)/(16)t=(\pi)/(2)+(\pi-0.201) \\ t=((\pi)/(2)+(\pi-0.201))/((\pi)/(16)) \\ t=22.98\text{ seconds} \end{gathered}`

Therefore, the person on the Ferris wheel will be 63 ft above the ground at;

`\begin{gathered} t=9.03\text{ seonds} \\ \text{and} \\ t=22.98\text{ seconds} \end{gathered}`