Given:
The radius of the Ferries wheel is 9.5m.
The number of second the ferries wheel take to rotate fully =10 seconds.
Aim:
We need to find the numeric model for the given situation.
Explanation:
The full rotation is 360 degrees.
The wheel rotates 360 degrees per 10 seconds.
Divide 360 by 10, we get
[tex]\frac{360}{10}=36^{o\text{ }}\text{ per second.}[/tex]
The wheel rotates 36 degrees per second.
Take that we traveled t seconds.
The point on the circle is y.
The angle is 36t degrees.
The height from the ground is 9.5+h.
The radius is 9.5m.
Consider the triangle that makes an angle of 36 t degrees,
Adjacent side = 9.5-h m and hypotenuse is 9.5 m.
Consider the cosine formula.
[tex]\cos \theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
Substitute adjacent side = 9.5-h m and the hypotenuse is 9.5 m.
[tex]\cos 36t^o=\frac{9.5-h}{9.5}[/tex]
[tex]\cos 36t^o=\frac{9.5-h}{9.5}[/tex]
[tex]9.5\cos 36t^o=9.5-h[/tex]
[tex]h=9.5-9.5\cos 36t^o[/tex]
The graph of the function is
