Question

A ferris wheel having a 60ft. diameter sits 4 feet above the ground and completes one cycle every four minutes. You find yourself at the top of the ferris wheel 75 seconds after the ride begins. Write a sinusoidal model of this situation.

Answer 1

\[y = A \sin(Bt+C) + k\]
vertical shift is 34 --> k = 34
radius of wheel is 30 ---> A = 30
period (time for 1 cycle) is 4 --- > B = 2pi/4 = pi/2

to find C use given point (1.25, 64)
** 75 sec = 1.25 min **
you are at top when angle is pi/2
Bt + C = pi/2
(pi/2)1.25 +C = pi/2
C = -pi/8\[y = 30 \sin( \frac{\pi}{2} t - \frac{\pi}{8}) + 34\]

Answer 2

Thank you very much!

Answer 3

yw
it helps to start with general sinusoidal function then try to find each coefficient using given information, work it out step by step