Help Problem involving a landing aircraft.

[International87]

I have 2 problems that are giving me trouble regarding the takeoff anf landing of an air craft. Here are the stats I have so far:
Takeoff speed: 33.7m/s
Takeoff angle:35 degrees
Landing speed: 37.3m/s
Maximum Abort speed:30.07m/s
Engine Thrust: 1,500N
Mass of Aircraft: 1060kg
Braking coeficient of friction: 0.30
Distance until takeoff:1216.71m
Time until takeoff:24.07s
Acceleration:1.4m/s squared


I need to know the final stopping point after the plane lands assuming it lands at its inital starting point,friction factored in. I also need to know the abort point incase the plane needs to make a sudden stop during take off. So essentially if the pilot stops before take off how much distance is needed beore the plane fully stops.

The abort velocity is a point during takeoff when the pilot must shut down and come to a complete stop or if the point is passed, take off. The runway must be long enough for the pilot to use reverse engine thrust and braking friction to stop safely if the decision is made not to take off.

Any help on what equations I need to use and how to approach these problems, they have given me a lot of trouble

 

[Mindscrape]

Try starting with Newton's Laws, the second law and some force diagrams should be particularly helpful. Then you can move into kinematics and plugging information in.

 

[International87]

What would F normal be for the force diagram? The wieght of the plane of the engine thrust? once I find that I can find the force of friction. Now how can i factor the force of friction into an equation to find the distance when landing? whta equation would I use to use the force of friction when determining the abort distance? Thank you for your help!

 

[Mindscrape]

Hmm, since they don't give any information about the lift then I suppose you can inaccurately use the weight of the aircraft for your force normal to the plane (math plane). So the first part should be pretty easy, if I'm not missing something. You'll want to find the decceleration due to the force of friction, and with the landing velocity determine how far it goes until it stops.

Now for the second part, they give you the takeoff angle, so I'm not sure if you are supposed to do something with related rates and takeoff angle, or what. Basically, the straightforward approach would be to find the distance (using force diagrams) that the pilot has to go with reverse thrust and braking in order to stop. Then from there find the maximum possible distance the pilot can go in order to perform the operation. I'm not sure if that would be right though, and whether you have to do something with takeoff angle.

Tinker with a bit and see if you can figure it out.

 

[International87]

Thank you very much you've been a great help, your information is much appreciated.

 

[International87]

I'm not ver strong with force diagrams and solving things graphicaly, I prefere algebraic solutions, anyone know of any equations i could use involving distance and friction?