Homework Sourseferris wheeldiameter100 meters 17 minute for one resolution
ferris wheel(diameter:100 meters, 17 minute for one resolution):
a) Assume that you get on the wheel at the bottom and that the wheel turns counterclockwise. Let (f)t be your height above the ground (be sure to state the units) at time t, the number of minutes since you got on the wheel. Create a table for this function showing four complete revolutions of the wheel
b) Plot the data from your table,label the axes and the scale on each axis.
c) Is your function periodic? Explain.
d) Sketch your best estimate of the graph of the function.
e) Identify the midline, amplitude, and period of your function.
f) Write a possible equation for your function.
Solution
Solution:
There isa way to do this. It involves finding f(t) explicitly.
This is because a period of 7 minutes is an awkward number to find the table bit by bit,
Here, if don\'t specify a unit, distances are in ft, angles in radians, angular velocity is in radians per minute and
times are in minutes.
Well, the y-coordinate of a circle is given by the sine function,
So if the circle\'s centre\'s height were 0 ft,
The function would be f(t)=Asin(wt+a0) for appropriate choices of A (determined by the size of the wheel),
w (determined by the frequency the wheel turns at) and
a0 (determined by the initial value t=0).
Then we just the distance from the ground to the centre (it\'s 10 foot from the ground with a 70ft radius so, 80ft) to
that.
So f(t)=80+Asin(wt+a0).
We want the adjustment to 80 to vary between -70 and 70. Since -1 <= sin(x) <= 1, we have A=70.
When t=0, we want to get on at the bottom, ie sin=-1. So sin(a0)=-1. Assuming 0<=a0<2pi, a0 = 3pi/2.
Now we find w, the angular velocity:
f(t)=80+70sin(wt+3pi/2)
We know that the period is 7 minutes. So w=2pi/7 so that f(0)=f(7)=f(14)=...
So The function is f(t)=80+70sin(2pi*t/7+3pi/2).
From these values (A,w), you can find the amplitude, midline and period.
Can sub in f(0),f(1),... for your table, too.
f(t)=80+70sin(2pi*t/7+3pi/2)
