Question

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds?

Answer 1

Answer:

$y=6sin(\frac{\pi}{4}t)$

Step-by-step explanation:

This problem is about an harmonic movement. The definition, that relates the given variables in this kind of movement is:

$y=Asin(\omega t)$

Where $y$ is the vertical displacement, $t$ is the time and $\omega = \frac{2 \pi}{T}$

So, we just have find the angular frequency and then replace all given values:

$\omega = \frac{2 \pi}{T}=\frac{2 \pi}{8}=\frac{\pi}{4}$

In this case, the period $T$ is 8 seconds, because according to the problem, half period is 4 second, from the highest point to the lowest, which is half of the complete period.

Now, replacing values:

$y=6sin(\frac{\pi}{4}t)$

This expression, where $y$ is the height or vertical displacement, gives the height at any point.

Answer 2

Answer:

h= 6 sine (pi/4 times t)