Creating Cubic Function to model flight path of jet

[sarahxox]

You are flying horizontally from Los Angeles To South Lake Tahoe. Just above Little Round Top you approach South Lake Tahoe from the southwest. The jet is flying 200mph.

1) Make a cubic function y(x)=ax[sup:1e6stc63]3[/sup:1e6stc63]+bx[sup:1e6stc63]2[/sup:1e6stc63]+cx+d, that describes your flight path altitude as a function of distance x, from the airport runway as you descend to land at South Lake Tahoe airport. Avoid crashes and unsafe conditions.

2) Assume the plane has a constant speed, horizontally, of 200mph. from the max vertical acceleration that the passengers will experience during the descent.

NOTE: you may choose to use google maps to get elevation information and horizontal distance approximations to complete this problem.

Using google maps I found the elevation of little round top peak to be about 8400 ft and the elevation of the airport to be 6000 ft.
I have no idea where to start.
I know somewhere I can use related rates...

 

[royhaas]

Re: Creating Cubic Functions

You need four points to completely specify a cubic equation. Note that the first derivative of distance with respect to time gives speed and the second derivative gives acceleration.

 

[sarahxox]

Re: Creating Cubic Functions

how do i find the four points with just locations on a map?

 

[Deleted member 4993]

Re: Creating Cubic Functions

You are flying horizontally from Los Angeles To South Lake Tahoe. Just above Little Round Top you approach South Lake Tahoe from the southwest. The jet is flying 200mph.

1) Make a cubic function y(x)=ax[sup:3moy8twn]3[/sup:3moy8twn]+bx[sup:3moy8twn]2[/sup:3moy8twn]+cx+d, that describes your flight path altitude as a function of distance x, from the airport runway as you descend to land at South Lake Tahoe airport. Avoid crashes and unsafe conditions.

2) Assume the plane has a constant speed, horizontally, of 200mph. from the max vertical acceleration that the passengers will experience during the descent.

NOTE: you may choose to use google maps to get elevation information and horizontal distance approximations to complete this problem.

Using google maps I found the elevation of little round top peak to be about 8400 ft and the elevation of the airport to be 6000 ft.
I have no idea where to start.
I know somewhere I can use related rates...

You don't need four points from map - you need four conditions.

For example,

at the point of landing, --> x=0 and y=0

also at the point of landing --> x = 0, y' = 0

Now decide on other two conditions - at the point of begining of descent.

 

[sarahxox]

Re: Creating Cubic Functions

Okay so I just pick random numbers like... -4x[sup:1ylxh7za]3[/sup:1ylxh7za]-2x[sup:1ylxh7za]2[/sup:1ylxh7za]+x-2

 

[Deleted member 4993]

Re: Creating Cubic Functions

Okay so I just pick random numbers like... -4x[sup:3gco6mwm]3[/sup:3gco6mwm]-2x[sup:3gco6mwm]2[/sup:3gco6mwm]+x-2

Absolutely not!