Question 20

Explanation

Determine Amplitude

Amplitude ($A$) is half the vertical distance between the crest and trough of the wave.

Given the distance from crest to trough is $16 \text{ meters}$.

Determine Period

Period ($T$) is the time required for one full wave cycle (e.g., from crest to crest).

Given the time from crest to crest is $12 \text{ hours } 24 \text{ minutes}$. We need to convert this to decimal hours.

Determine Wave Function

The wave height function can be modeled with a sine function:

Substitute the values $A = 8$ and $T = 12.4$:

Thus, a possible wave height function is $h(t) = 8 \sin\left(\frac{2\pi}{12.4} t\right)$.