Q41. - Algebra 2

Question

For Exercises $39-41$, use the following information.

A marker buoy off the coast of Gulfport, Mississippi, bobs up and down with the waves. The distance between the highest and lowest point is 4 feet. The buoy moves from its highest point to its lowest point and back to its highest point every 10 seconds.

What is the height of the buoy after 12 seconds?

Step-by-Step Solution

Answer

The height after $12$ seconds is $1.9 feet$

Step 1. Given information

A bouy with difference of $4$ feet is given

Step 2. Concept used

Put the value of time in the equation-

$y=2\sin \frac{\pi }{5}t$

Do calculation.

Step 3. Calculation

The equation is-

$y=2\sin \frac{\pi }{5}t$

The time given is $12$ seconds-

 $\begin{array}{l}y=2\sin \frac{\pi }{5}t\\ =2\sin \left(\frac{\pi }{5}\times 12\right)\\ \approx 1.9\end{array}$

The height is $1.9 feet$