Question

a ferris wheel has a 48-foot radius and the center of the ferris wheel is 52 feet above the ground. the ferris wheel rotates in the ccw direction at a constant angular speed of 2 radians per minute. shane 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. write an expression (in terms of t ) to represent the number of radians shane has swept out from the 3-o'clock position since the ride started.

Answer 1

2π/40t

Step-by-step explanation:

There are 2π radians in a full rev

2πR/3 Rev/ min = 2/3π minutes per rev

R= 2.0944 min per rev

Period is 2/3π

2π/x = 2/3π

∴ x = 3

∴sin xt = sin 3t

He starts at 3 o'clock position which is 1/2 way between low and high points, so there is no phase shift

Amplitude = 44

44 sin 3t = height above center

Height above ground is shifted by 48 feet up from center

∴ 44 sin (3t) + 48 would be height above ground ( at time = 0 he is 48 ft above ground)