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Suppose Ken is riding a Ferris wheel.  The maximum height he attains is 16 m and the minimum height is 0 m.  The time it takes to make one cycle is about 6 minutes.  Draw a graph which represents this scenario if Ken starts at a height of about 8 m.

 

Please can you explain how you know to use what points.

Julius  May 19, 2017
edited by Julius  May 19, 2017
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Here's the graph you need : https://www.desmos.com/calculator/e3rve2bfvr

 

Using  y  =  Asin (Bx + C)  + D

 

We can divide the normal  period of the sine  (2 pi)  into  6  equal parts....so that  each part (one minute)  is  [2pi / 6] rads   =  pi/ 3  rads  =  B.......

 

After 1.5 minutes  the normal sine will reach its max height  = 1

Note..... sin [  pi (1.5)/3]  =

sin (pi/2)  =  1 

 

And it will return to the midline point of y= 0  after 3 minutes since sin (pi (3)/ 3)  = sin (pi)  = 0

 

And it will reach a minimum of y = -1 after 4.5 minutes  because sin (pi (4.5)/3)  = sin (3pi/2)  = -1

 

And it returns to the midline  (the starting height) of y = 0  at  6 minutes since sin (pi * 6/ 3)  =

sin (2pi)  =  0 

 

There is no shift left or right, so  "C"  = 0 

 

Next we need to make some adjustments

 

We know  that the amplitude  is 8  because the graph rises 8 units up and down from the midline of y = 0 ....so "A'  = 8

 

But......the midline  of the graph starts at 8  so  we need to append 8 to the function.....so, "D'"  = 8  will give us that shift

 

I hope that helps   ....!!!!

 

 

cool cool cool

CPhill  May 19, 2017

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