A Ferris wheel is 26 meters in diameter and the bottom of th

A Ferris wheel is 26 meters in diameter and the bottom of the Ferris wheel is 8 meters above the ground. You board the Ferris wheel at the 3 o\'clock position. a. The wheel completes one full revolution every 4.2 minutes. What is the angular speed (in radians per minute) that the Ferris wheel is rotating? radians per minute b. Write a formula that gives the angle measure (in radians) swept out from the 3 o\'clock position, a, in terms of the number of minutes elapsed since you boarded the Ferris wheel, t. a(t) = (2pi/4.2) t syntax ok c. Define a function f that gives your height above the ground (in meters) in terms of the number of minutes elapsed since you boarded the Ferris wheel, t. f(t) = 13 cos(2pi/4.2) + 8 syntax ok

Solution

Ans(b):
we know that one complete revolution makes angle of 2pi radian at the center of wheel.
Given that one revolution is completed in 4.2 minute
so angle traversed in 1 minute 2pi/4.2
then angle traversed in t minute (2pi/4.2)t

Then required formula for angle measure (in radians) swept out from 3 o\'clock position is given by
(2pi/4.2)t

Ans(c):

given diameter is 26 meters.
then amplitude fill be half of 26 which is 13 meters.

Clearly at 3 o\'clock, angle will be 0.
we know that sin(theta) gives 0 when angle is 0
so we use sine formula

given that bttom of the wheel is 8 meter above ground while the sine function will count your positoin with respect to center of the wheel.
so actual height should be 8+13(radius) =21

Then required function will be
f(t)=13*sin ((2pi/4.2)t)+21