Hello, mathaddict!

Juliana gets into the seat at the bottom of a Ferris wheel 1.5 m above the ground.

The radius of the Ferris wheel is $\displaystyle r$ m and it rotates in an CCW direction.

(a) Find the height, $\displaystyle h$, of Juliana from the ground when the Ferris wheel stops

after rotating 300°. (Give your answer in terms of r.) Code:

* * *
* *
* *
* *
* P *
* o *
* r / | *
/60°|½r
* / |C *
A o - - - o - - - *
: * | *
: * * *
h : |
: |1.5
: |
- - o - - - o - - - - - -
B D

The center of the Ferris wheel is $\displaystyle P.$

The radius is: $\displaystyle r = PA$

$\displaystyle \angle APD = 60^o$

In right triangle $\displaystyle PCA,\;OC \:= \:r\cos60^o \:=\:\frac{r}{2}$

Hence: .$\displaystyle h \;=\;AB \;=\;PF - PC \;=\;(r + 1.5) - \frac{r}{2}$

. . Therefore: .$\displaystyle \boxed{h \;=\;\frac{r+3}{2}}$