Finding the Landing Path of an Airplane Using Cubic Polynomial Functions

In summary, the conversation discusses finding the derivative of a cubic polynomial function and using the values to show a simplified equation. The main problem is solved by realizing that c=0 and using the given information to solve for a and b. The person asking for help is grateful and relieved to have their problem solved.
  • #1
wisredz
111
0
Hi I have this question that is driving me mad any help is appreciated.

An airplane is flying at altitude H when it begins its decent to an airport runway that is at horizontal ground distance L from the airplane. Assume that the landing path of the airplane is the graph of a cubic polynomial fuction y=ax^3+bx^2+cx+dwhere y(-L)=H and y(0)=0.

(a) What is dy/dx at x=0?
(b) What is dy/dx at x= -L?
(c) Use the values for dy/dx at x=0 and x= -L together with y(0)=0 and y(-L)=H to show that

y(x)=H[2(x/L)^3+3(x/L)^2]

Anyhelp is appreciated. Thanks in advance
 
Last edited:
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  • #2
Btw, that dy/dx at x=0 equals c and that dy/dx at -L equals 0 is clear to me. My problem is that I cannot use those informations...
 
  • #3
now at the top and bottom it is flat so dy/dx at x=0 and x=-L should be zero,
 
  • #4
oh u posted again,
[tex] y= ax^3+bx^2+cx[/tex]
on Solving u will have c=0
Therefore
[tex] y= ax^3+bx^2[/tex]
u can get values of a and b from
dy/dx at x= -L, is zero
and also y(-L) = H
 
  • #5
God, it is that easy then... It was 2 in the morning here(Turkey) Thanks a lot, I was going out of my mind.
 

What is the purpose of an airplane landing path?

An airplane landing path is the designated route that an aircraft follows to safely land at an airport. It is designed to ensure that the aircraft can reach the runway at the appropriate speed and angle for a safe landing.

How is an airplane landing path determined?

The landing path is determined by various factors such as the aircraft's weight, speed, wind conditions, and runway length. Pilots also consider other factors like terrain, obstructions, and noise abatement procedures when selecting the best landing path for a specific airport.

What are the different types of airplane landing paths?

There are three main types of airplane landing paths: visual, instrument, and precision. Visual landing paths are used when visibility is good and pilots can rely on their own judgement to land the aircraft. Instrument landing paths use navigation aids and instruments to guide the aircraft to the runway. Precision landing paths are used in low visibility conditions and require more advanced equipment to guide the aircraft to a precise landing.

How does weather affect an airplane landing path?

Weather conditions play a crucial role in determining the appropriate landing path for an aircraft. Strong winds, heavy rain, or low visibility can affect the aircraft's ability to safely land and may require the use of different landing procedures. Pilots carefully monitor weather conditions and adjust the landing path accordingly to ensure a safe landing.

What safety measures are in place to ensure a safe airplane landing path?

Airports and aviation authorities have strict safety regulations in place to ensure a safe airplane landing path. This includes regular maintenance of runways, navigation aids, and other equipment, as well as training for pilots and air traffic controllers. Airports also have emergency procedures in place in case of unexpected events during a landing.

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