- #1

Ryaners

- 50

- 2

## Homework Statement

The height in meters of a person off the ground as they ride a Ferris Wheel can be modeled by:

h(t) = 18 · sin[(π · t )/ 7] + 20

where t is time elapsed in seconds. If h is restricted to the domain [3.5, 10.5], find and interpret the meaning of h

^{-1}(20).

## The Attempt at a Solution

Here are my workings:

Let y = h(t)

y = 18⋅Sin[(π⋅t)/7] + 20

(y - 20) / 18 = Sin[(π⋅t) / 7]

arcsin [(y - 20) / 18] = (π⋅t) / 7

π⋅t = 7⋅{arcsin [(y - 20) / 18]}

t = (7/π)⋅{arcsin [(y - 20) / 18]}

⇒ h

^{-1}(t) = (7/π)⋅{arcsin [(t - 20) / 18]}

⇒ h

^{-1}(20) = (7/π)⋅arcsin(0) = 0

However this is the solution given:

h

^{-1}(20) = 7

"This means that a height of 20 meters is achieved at 7 seconds in the restricted interval. In

fact, it turns out that h

^{−1}(t) = 7 · {π − arcsin[(t − 20)/18]}/π when h is restricted to the given

interval."

I'm not sure why my approach is incorrect; any pointers would be much appreciated!