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=15cos(pi/20)t. how long does it take for the waterwheel to complete one turn?
a) 5sec
b) 10sec
c) 20sec
d) 40sec

Answer 1

Answer:

d) 40 sec

Step-by-step explanation:

We have been given that 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 $h=15cos(\frac{\pi}{20})t$. We are asked to find the time it will take for the waterwheel to complete one turn.  

To solve for time we need to find the period of the given cosine function.

We know that general form of a cosine function is in form $y=a\cdot\text{cos}(bx)+c$, where,

a = Amplitude,

$\text{Period}=\frac{2\pi}{b}$

We have been given $b=\frac{\pi}{20}$. Substituting this value in period formula, we will get:

$\text{Period}=\frac{2\pi}{\frac{\pi}{20}}$

$\text{Period}=\frac{20*2\pi}{\pi}$

$\text{Period}=20*2$

$\text{Period}=40$

Therefore, it will take 40 seconds for the waterwheel to complete one turn and option 'd' is the correct choice.