Thread: HW Help Trig Modeling

Need help with this problem:

1) A plane flying 300 miles from Detroit to Chicago has been put in a holding pattern above the Chicago Airport. The holding Pattern is a circle with a diameter of 20 miles that the plane completes every 15 minutes. COmplete the following steps to write n equation that models the distance of the plane from Detroit as a function of time.
a) What is the period of this motion? Suggested ans by me : 2pi/15
b) What vertical stretch is needed to show the diameter of 20 miles? 310
c) what vertical shift is needed to show the 300 miles distance between the airports? 300
d) Write an equation modeling the plane's distance from Detroit while it is flying in this holding pattern.(sketch the equation)
Suggested ans: D(t) = -10cos (2pi/15)t + 300

Originally Posted by tictac

1) A plane flying 300 miles from Detroit to Chicago has been put in a holding pattern above the Chicago Airport. The holding Pattern is a circle with a diameter of 20 miles that the plane completes every 15 minutes. COmplete the following steps to write n equation that models the distance of the plane from Detroit as a function of time.
a) What is the period of this motion? Suggested ans by me : 2pi/15

I will guess that you are using "minutes" as your unit of time. (The exercise should have specified this!) If so, then your period looks good.

Originally Posted by tictac

b) What vertical stretch is needed to show the diameter of 20 miles? 310

How did you get an amplitude of 310...?

Originally Posted by tictac

c) what vertical shift is needed to show the 300 miles distance between the airports? 300

Three hundred sounds right. Then the plane's distance from Detroit will vary ten miles on either "side" of this distance.

Originally Posted by tictac

d) Write an equation modeling the plane's distance from Detroit while it is flying in this holding pattern.(sketch the equation)
Suggested ans: D(t) = -10cos (2pi/15)t + 300

Is there any particular reason you used an amplitude of minus ten? (The only difference between +10 and -10, or sine and cosine, will be where you "start" the plane in the holding pattern, but you might be asked to justify this choice.)

Thanks Stapel
a) Yes, minutes is the unit I used.

b) Typo! Should read 10.

c) OK

d) I used -10 because the holding pattern started at the bottom of the circle when the plane was 10 miles away from Chicago and 290 miles from Detroit.

Thanks again