Brian is riding a Ferris wheel. The wheel has a radius of 25 feet, and at his lowest point, Brian is 8 feet off the ground. Brian times how long it takes to travel from the lowest point to the highest point and finds that it takes 8 seconds. Write a sinusoidal equation to model Brian’s movement around the Ferris wheel.

Question

Reiny · Answer

I will use a sine curve

amplitude = 25
so let's start with y = 25 sin t , where t is in seconds
period = 16 seconds
2π/k = 16
16k = 2π
k = π/8
so far y = 25 sin π/8 t
we want the lowest point to be +8, so we have to raise the sine curve 33 units
so far: y = 25 sin π/8 t + 33

we want our lowest point to be +8 when t = 0
so we need a phase shift
y = 25 sin π/8(t + k)+ 33
8 = 25 sin (π/8)k + 33
-25 = 25 sin πk/8
sin πk/8 = -1
I know sin 3π/2 = -1
so πk/8 = 3π/2
πk = 12π
k = 12

y = 25 sin π/8(t + 12)+ 33
min = 8, max = 58, half way = 33

check at the main 4 intervals of a period
t = 0 ---> y = 25 sin(3π/2) + 33 = 8 , good
t = 4 ---> y = 25 sin(2π) + 33 = 33 , half way, good
t = 8 ---> y = 25sin (5π/2) + 33 = 58, good
t = 12 --> y = 25sin(3π) + 33 = 33 , good, coming back down
t = 16 --> y =25sin(7π/2) + 33 = 8 , back to the bottom,
ALL IS GOOD!

bobby · Answer

Thanks....got it