Question

A ferris wheel with a radius of 25 meters makes one rotation every 36 seconds. At the bottom of the ride, the passenger is 1 meter above the ground.

a) Let h be the height, above ground, of a passenger. Determine h as a function of time if h = 51 meter at t = 0.

b) Find the height h after 45 seconds.

Answer 1

a)
"P is the position of the passenger.

h is the height of the passenger with h=1+25+x

x depends on the angle of rotation A.

sin(pi/2 - A) = x/25 which gives x = 25 cos(A)

Angle A depends on the angular speed w as follows

A = w t where t is the time.

The angular speed w is given by

w = 2pi / 36 = Pi / 18 (radians/second)

We now substitute to find h as follows h(t) = 25 cos( (pi/18) t) + 26 , where t is in seconds and x in meters."

b) "h(45) = 25 cos( (pi/18) 45) + 26 = 25 cos(3pi/2) + 26 = 26 meters."