TRIG WHEEL 4
A Ferris wheel reaches a maximum height of 20 m. The lowest point of the wheel is 2 m above ground. The wheel completes two revolution in 1 minute (60 seconds). Model the wheel using a sine wave function starting at the same point as in previous activities. As before the function has amplitude (A), frequency (B), shift (C) (again this will be zero) and vertical shift (D).
The horizontal shift (C) is the most complicated and will be treated in the next section, Trig Wheel 5.
Draw a diagram to help you with the problem.
The horizontal shift (C) is the most complicated and will be treated in the next section, Trig Wheel 5.
Draw a diagram to help you with the problem.
Amplitude (A)
The amplitude is the radius of the circle or max - min divided by 2, which is (20 - 2)/2
= 9 m.
= 9 m.
frequency (B)
The frequency B is equal to the distance divided by the time for one period, which is:
horizontal shift (C)
As before we are dealing with a normal sine wave so there is no shift to be concerned with.
vertical shift (D)
Because the wheel has been lifted or 'shifted' vertically, the axle (circle origin) is now at a height of (max + min)/2 = (20 + 2)/2 = 11 m. So D = 11 and the equation for the function becomes.