Answer:
a)
b)
c) Is just a translation of th original graph.
Step-by-step explanation:
Data given
R= 60 ft represent the radius
D= 2*60 = 120 ft represent the diameter
Suspended x=10 ft above the ground
Rpm = 2 rev/6min = 1 rev/3 min
The friend start 1/4 after Sydney.
Part a
We can find the maximum and minimum point like this
We add 10 ft to the maximum because we are 10 ft above the ground
Then we can find the amplitude:
So then
And the middle point would be given by:
We have also the period given by since we have 1 revolution each 3 minutes.
We need to write a function that describes a Sydney’s height above the ground as a function of the number of seconds. So then we need to take the middle point 70 ft and subtract the function in terms of the amplitude and the period.
The the number of wave is given by
And the general equation would be given by:
And replacing we got:
Part b
For this case we just need to replace t =1.25 min and we got:
Part c
We need to take in count that the midpoint is at y=0. With the transofrmation we have the midpoint at y=70 ft. And if we move 1/4 we can see that the graph for the friend is the sine graph of the original equation.
And we can se this on the plot attached. When t=0 for the cos function is t=0.75 for the sin function. And the equation for the friend would be given by:
