Answer:
a) The expression for the change in angular position is
.
b) The expression for the height of Ryan regarding the center of the Ferris wheel is
.
c) The expression for the height of Ryan above the ground is
.
Step-by-step explanation:
The statement is incomplete. Complete form is introduced below:
<em>Kyle boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 5 radians per minute and has a radius of 40 feet. The center of the Ferris wheel is 47 feet above the ground. Let t represent the number of minutes since the Ferris wheel stated rotating.</em>
<em>a)</em><em> Write an expression (in terms of t) to represent the varying number of radians </em>
<em> Ryan has swept out since the ride started.</em>
<em>b)</em><em> Write an expression (in terms of t) to represent Ryan's height (in feet) above the center of the Ferris wheel.</em>
<em>c)</em><em> Write an expression (in terms of t) to represent Ryan's height (in feet) above the ground. </em>
a) Let suppose that Ferris wheel rotates counterclockwise. As the Ferris wheel rotates at constant rate, this kinematic expression can be used to determine the change in angular position (
), in radians:
(1)
Where:
- Angular velocity, in radians per minute.
- Time, in second.
If we know that
, then the expression for the change in angular position is
.
b) Geometrically speaking, Ryan's height with respect to the center of the Ferris wheel is described by the following formula:
(2)
Where:
- Radius of the Ferris wheel, in feet.
- Height of Ryan with respect to the center of the Ferris wheel, in feet.
If we know that
and
, then the expression for the height of Ryan regarding the center of the Ferris wheel is
.
c) We use the following geometric expression to model Ryan's height above the ground:
(3)
Where
is the height of the center of the Ferris wheel above the ground, in feet.
If we know that
,
and
, then the expression for the height of Ryan above the ground is
.