Question

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cosine (StartFraction pi Over 20 EndFraction t). How long does it take for the waterwheel to complete one turn? 5 seconds 10 seconds 20 seconds 40 seconds.

Answer 1

Solving the trigonometric equation, it is found that it takes 40 seconds to complete one turn.

The height is modeled by:

$h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}$

The initial height is $h(0) = 15$, hence, one turn is completed when h(t) = 15.

$h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}$

$15 = 15\cos{\left(\frac{\pi}{20}t\right)}$

$\cos{\left(\frac{\pi}{20}t\right)} = \frac{15}{15}$

$\cos{\left(\frac{\pi}{20}t\right)} = 1$

The length of one turn is of $2\pi$, and $\cos{(2\pi)} = 1$, hence, the solution is found according to:

$\frac{\pi}{20}t = 2\pi$

$t = \frac{40\pi}{\pi}$

$t = 40$

It takes 40 seconds to complete one turn.

You can learn more about trigonometric equations at brainly.com/question/24680641