Write a trigonometric function to model a Ferris wheels heig

Write a trigonometric function to model a Ferris wheels height over time H(t) for a Ferris wheel with a diameter of 110meters a height of 120m and takes 30 minutes to complete one cycle (bottom to bottom). H(t)=Asin(Bt+C)+D What will the height be at 13minutes?

Solution

H(t) = Asin(Bt +C) +D

Time period = 30 min.

B = 2pi/30 = pi/15

height, D = 120mt

A = 110/2 = 55 metres

ferris wheel is at t=0 H(t) =120mt

t = 30/4 sec ; H(t) = 175mt

t = 30/2 ; H(t) = 110 +120 = 230mt

t= 30 ; H(t) = 120 mt

Now we can model this by a cosine function H(t) = -55cos(pi*t/15) + 175

1) In terms of sine function H(t) = -55(sin(pi*t/15 +pi/2) + 175 mt

2) At t= 13min H(t) = -55sin(pi*13/15 +pi/2) +175 = 225.24 mt