Casey boards a Ferris wheel at the 3-o clock position and rides the Ferris wheel

Solution :

It is given that :

Casey boarded a Ferry wheel at position of 3 'o' clock.

The angular speed of the Ferry wheel = 5.6 radians per minute

The radius of the Ferry wheel = 50 feet

The height of the center wheel of the Ferry from the ground = 55 feet

Let the number of minutes be = t

a). The expression of the varying number of radians θ is given by :

After t minutes,  θ = angle swept

                           θ = 5.6 t radians

b). Finding the height from the center of the wheel.

We know that : y = r sin θ

Given r = 50 feet

So, y = 50 sin (5.6 t) feet

Therefore, the height above the ground can be found by :

h = y + 55 (from ground)

h = 50 sin (5.6 t) + 55   feet