Question

Can you solve this for me briefly and without being too detailed?

Answer 1

`h(t)=9\sin (((\pi)/(5))t-(\pi)/(2))+10`

Check the graph below, please.

1) From this problem, we can see that the amplitude is given by the radius of 9.5m. Since this Ferris wheel rotates at once every 10 seconds, then we can write out the period as 10. Adding the period to the 1.2 meters above the ground yields us the midline: 9+1.2= 10.2

2) From this we can write out the following:

Period:

`\begin{gathered} P=(2\pi)/(B),10=(2\pi)/(B) \\ 10B=2\pi \\ B=(2\pi)/(10) \\ B=(\pi)/(5) \end{gathered}`

Phase Shift (C):

`h(0)=1.2,C=-(\pi)/(2)`

a) So we can write out the following equation:

`\begin{gathered} h(t)=A\sin (((2\pi)/(B))t+C)+D \\ h(t)=9\sin (((\pi)/(5))t-(\pi)/(2))+10 \end{gathered}`

So this is the sinusoidal function (sine) with the height in meters, and time in seconds.

b) Let's sketch the graph for this sinusoidal function, considering two complete cycles:

Note that since the period is 10, we have two cycles when x=20.