Abuoy oscillates in simple harmonic motion y= a cos cos as waves move past it. the buoy moves a total of 3.5 feet (vertically) from its low point to its high point. it returns to its high point every 10 seconds.
(a) write an equation describing the motion of the buoy if it is at its high point at t=0
(b) determine the velocity of the buoy as a function of t.

a)

b)

Step-by-step explanation:

Part a

Since the buoy oscillates in simple harmonic motion the equation to model this is given by:

For this case from the info given we know that:

"It returns to its high point every 10 seconds." That means period =10 , and the angular frequency can be founded like this:

Assuming that the value for the phase is our model equation is given by:

Part b

From definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this:

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

you already gave the answer

step-by-step explanation: