What is the equation of the height of a person in a Ferris wheel in the following case?As the person rides a Ferris wheel, the height from the...

We have the highest point that a person in the Ferris
wheel reaches as 43 feet. The diameter of the Ferris wheel is 40 feet. And the time
taken to make a revolution is 8 seconds. It is also given that the highest point is
reached in 3 seconds.

The function of the distance from the
ground with respect to time is d (t) = 23 - 20*(sin ((3/4)*pi +
(2/8)*pi*t))

Here the sine term in the
function contributes the value that oscillates from -20 to + 20; the 23 ensures that the
distance stays between 3 and 43.

The lowest value that d
(t) reaches is when the sine term is -20. Here the height is 23-20 = 3 feet. The highest
value is when the sine term is + 20; here it is 20 + 23 = 43 feet. The highest point is
reached after 3 seconds and one revolution is completed in 8
seconds.

The value of the function only takes positive
values as the height of the person from the ground cannot be negative (else s/he would
be underground!)

If you want to know the distance at
different values of t, just substitute t with that value and solve the
function.