Use the following information to answer the next question. A Ferris wheel at an amusement park, with a diameter of 12 m, can be modeled using the equation h(t) = - 6 cos(π/20)*t+9 is the...

 
Use the following information to answer the next question.
A Ferris wheel at an amusement park, with a diameter of 12 m, can be modeled using the equation h(t) = - 6 cos(π/20)*t+9 is the height above the ground in metres, and t is the time in seconds.
 
3.The number of seconds required for a rider to reach a height of 14 m for the first time is, to the nearest tenth,
A.16.3 s The answer is A
B.16.5 s
C.20.4 s
D.932
Answer: Substitute the height of 14 m for h(t),then graph both sides and find the point of intersection. Thex-value will give the time 14 m is first reached.
14 = - 6 cos(π/20)*t+9

t= 16.3 sThe answer is A

I dont know how to to solve this!

Should I do this?

Y1=- 6 cos(π/20)*t+9

Y2=14

and find the t using my calculator

Calculate 5:intersect???

Please help!

 

1 Answer | Add Yours

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

We are given the model for the height at time t (in seconds) as

`h(t)=-6cos(pi/20)t+9`

We are asked for the first time that the height is 14.

The height varies from a minimum of 3ft to a maximum of 15 feet. At time t=0 it begins at the minimum. The period is 40 seconds, so the height will be 14ft twice in that first 40 seconds.

One way is as you have suggested. Graph y=h(t) and y=14 and find the intersection. In a TI-8X you would graph the two functions, making sure that the intersection appears in the viewing window; then hit 2nd trace and #5 intersect. The calculator will have you affrim the two functions and ask for an initial guess. The calculator will return 16.27141 so the answer will be 16.3 seconds.

If you are not allowed to use a graphing calculator, set h(t)=14:

`14=-6cos((pi/20)t)+9`

`5=-6cos((pi/20)t)`

`cos((pi/20)t)=-5/6`

`pi/20 t=cos^(-1)(-5/6)`

`pi/20 t~~2.55590711`

`t~~51.1181422/pi~~16.27141003`

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