Question

On a windmill, the tip of one blade moves in a circular motion. The maximum height is 18 feet and the minimum height is 4 feet. The height of the tip of the blade (in feet) can be modeled by the function h(x)=−14sinx+18 h(x)=−14sinx+18 where x is time in seconds. Use the inverse function to determine how many seconds it will take to make a full rotation for one blade.

A 0.3 second


B 0.6 second


C 1.6 seconds


D 3.2 seconds

Answer 1

The correction is D

Explanation:

From the question we are told that

The maximum height is
`h_m = 18 ft`

The minimum height is
`h_i = 4 ft`

The function that models the height of the blade is
`h(x) =- 14 sin(x) + 18` here x is time in seconds

Now at maximum height

`18 = - 14 sin(x) + 18`

=>
`-14 sin(x) =0`

=>
`sin(x) =0`

=>
`x =sin^(-1)[0]`

=>
`x =0 \ s`

Now at minimum height

`4 = -14 sin(x) + 18`

=>
`-14 = -14 sin(x)`

=>
`sin (x) = 1`

=>
`(x) = sin^(-1)[1]`

=>
`x = 1.6 \ s`

Now this values is the time taken to move from the higher position of the blade to the lower position of the blade

Now it will take this same amount of time to complete the circle

So the total time take is

`x_t = 2 * |x|`

=>
`x_t = 2 * 1.6`

=>
`x_t = 3.2 \ s`