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? h = 4 sine (startfraction pi over 6 endfraction t) h = 4 sine (startfraction pi over 3 endfraction t) h = 6 sine (startfraction pi over 4 endfraction t) h = 6 sine (startfraction pi over 2 endfraction t)

Answer 1

The equation of the model h will be h = 6 × sin(2πt/8). Then the correct option is C.

What is a function?

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

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.

Then we have

$h=A \times \sin \omega t, \ \ at=0, \ \ h =0$

The maximum displacement of the buoy in either direction is 6 ft, then we have

$h=6 \times \sin \omega t$

The time it takes the buoy to get from the lowest to the highest point is 4 seconds then the oscillation time period will be 8 seconds.

Then we have

$\omega T = 2\pi\\\\\omega = \dfrac{2\pi}{8}$

Then the h will be given as

$h =6\times \sin (\dfrac{2\pi}{8}t)$

More about the function link is given below.

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