Question

A Ferris wheel has a 40-foot radius and the center of the Ferris wheel is 48 feet above the ground. The Ferris wheel rotates in the CCW direction at a constant angular speed of 2 radians per minute. Enrique 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 Enrique has swept out from the 3-o'clock position since the ride started.

Answer 1

`\theta=(\pi)/(4)+2(rad)/(s)t`

Step-by-step explanation:

To find the expression in terms of time t you take into account the following equation for the angular distance traveled by an object with angular acceleration w and initial angular position θo:

`\theta=\theta_o+\omega t+(1)/(2)\alpha t^2` ( 1 )

α is the angular acceleration, but in this case you have a circular motion with constant angular speed, then α = 0 rad/s^2. θo is the initial angular position, the information of the question establishes that Enrique is at 3-o'clock. This position can be taken, in radian, as π/4 (for 12-o'clock = 0 rads).

The angular speed is:

`\omega=2(rad)/(min)`

You replace the values of θo, α and w in the equation ( 1 ):

`\theta=(\pi)/(4)+2(rad)/(s)t`

Furthermore, the arc length is:

`s=r\theta=(40ft)[(\pi)/(4)+2(rad)/(s)t]`