Question

The blades of a windmill turn on an axis that is 40 feet from the ground. The blades are 15 feet long and complete 3 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.

a is the .
The vertical shift, k, is the... length of a blade, height of a windmill, or numbers of rotations per minute.
a =
k =

Answer 1

Draw a diagram (shown below) to illustrate the problem.

The rotational speed is
ω = (3 rev/min)*(1 min/60 s)*(2π rad/rev) = π/10 rad/s
The period is
T = 2π/ω = 20 s

The amplitude of the rotational motion is equal to the radius of 15 ft.

At t=0, the height of the tip of the blade is horizontal to the right, therefore its motion relative to the ground is given by
$y=15 sin( \frac{ \pi t}{10})+40$

A plot of the motion is shown below.

Answer 2

20

5

30

Step-by-step explanation: