Question

Ferris wheel has a 108-foot diameter and the center of the Ferris wheel is 58 feet above the ground. The Ferris wheel rotates in the CCW direction at a constant angular speed of 6 radians per minute. Chance boards the Ferris wheel at the 3-o'clock position and rides the Ferris wheel for many rotations. Let t represent the number of minutes since the ride started.

Required:
a. Write an expression (in terms of t) to represent the number of radians Justin has swept out from the 3-0'clock position since the ride started.
b. How long does it take for Justin to complete one full revolution (rotation)?
c. c. Write an expression (in terms of t) to represent Justin's height above the center of the Ferris wheel (in feet)

Answer 1

a. θ = 6t

b. 1.048 minutes

c. y = 54sin(6t)

Explanation:

diameter d = 108 foot

distance above the ground = 58 feet

a.) expression to represent number of radians

radian = 6 rad/min

θ = wt

w = 6

θ = 6t

t is in minutes

b.) we are to find the time period for one full revolution

time period = 2π/6

π = 22/7

`T=(2(22/7))/(6)`

= 1.048 minutes

c. Expression showing Justins height above the ground

y = rsinθ -----(1)

θ = wt = 6t

we find the radius r

diameter = 2 * radius

108 = 2r

r = 108/2

= 54 foot

we put these values in the equation 1 above

y = 54sin(6t)