A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 5.5 feet from its low point to its high point, and that it returns to its high point every 8 seconds. Write an equation that describes the motion of the buoy if it is at its high point at time t = 0.

Step-by-step explanation:

Let's take the equation for the height of a buoy:

d = Acos(wt)

Where

(We divided by 2 because there are 2 directions for the magnitude of total displacement, which is the amplitude of a periodic function)

 where T = 8 seconds

Lets substitute the values, in the equation, we have:

Therefore, the equation that describes the motion of the buoy if it is at its high point at time t = 0 is

a² + b²= c²

24² + 7² = c²

c= 25

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles