Write an Equation

Question

Sarah is riding a ferris wheel. She gets on at the bottom of the ride 1 m above the ground. Exactly one minute later, she has rotated 3/4 of a rotation, and she is 9 m above the ground. Write an equation to fit this curve, where x is time in seconds and y is height in meters. 

Answer 1

Hello Amber,

 

I wish there was an easy method to insert a diagram. Will make the best of what we have.

 

Let y be the height of  Sarah from the ground (in M) at time x (min.)

 

At x=0, y=1m and at x = 1, y= 9 m

 

Let the angle made by the radius, connected to Sarah at some intermediate time, with the Vertical be A (A=0° when x=0 and A= 270° when x = 1)

 

Then y = 1 + 8(1-cosA) since A =270x° we get y= 1+ 8(1-cos(270x))

Hope this helps.

 

I would be interested in Online tutoring.

Wish you the best.

Pradip