Solving the trigonometric equation, it is found that it takes 40 seconds to complete one turn.
The height is modeled by:
[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
The initial height is [tex]h(0) = 15[/tex], hence, one turn is completed when h(t) = 15.
[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
[tex]15 = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
[tex]\cos{\left(\frac{\pi}{20}t\right)} = \frac{15}{15}[/tex]
[tex]\cos{\left(\frac{\pi}{20}t\right)} = 1[/tex]
The length of one turn is of [tex]2\pi[/tex], and [tex]\cos{(2\pi)} = 1[/tex], hence, the solution is found according to:
[tex]\frac{\pi}{20}t = 2\pi[/tex]
[tex]t = \frac{40\pi}{\pi}[/tex]
[tex]t = 40[/tex]
It takes 40 seconds to complete one turn.
You can learn more about trigonometric equations at https://brainly.com/question/24680641
