Calculating Takeoff Time and Distance for a Plane on a Runway

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In summary, the plane needed to take off in 720 seconds, but it only took 26.8 seconds due to the plane's required velocity.
  • #1
cool_dude
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Homework Statement


A plane accelerates from rest at a constant rate of 5.00 m/s^2 along a runway that is 1800 m long. Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time t_{TO} needed to take off?


Homework Equations


i think the formula I'm supposed to use is d = vt + 1/2at


The Attempt at a Solution


not exactly sure if this is the correct formula but that's what i thought i have to use. we know that d = 1800m and we know that initial velocity = 0 and a = 5 m/s^2 so then we isolate for t. thus we get t = 1800 / 2.5 = 720. however i think this might be wrong because i don't think its realistic for a plane to take 12 minutes on the run way to take off. any ideas?


Also part of the question was What is the distance d_last traveled by the plane in the last second before taking off?

I tried to use the same formula d = vt + 1/2at and since we figured out time from part a we sub (t - 1) into here and get distance traveled in the last second before taking off. not sure if any of this is right. can someone verify?

Thank you
 
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  • #2
your equation is wrong. it should be:

d = v0*t + (1/2)at^2


you didn't have the t^2...

pluggin in t-1... gives the distance traveled in the first t-1 seconds... not the last 1 second. you're close...
 
  • #3
oops you i forgot the square. so then i get 26.8 seconds. does that make sense for a plane to take amount of time for lift of? i think it makes sense to me. not sure. also does this mean that we don't care about the required velocity for takeoff?

hmmm the second part is tricky. i thoght that t - 1 would mean that let's say it took 10 seconds then t = 10 and the second before it is t - 1 = 9. I'm a bit confused on this part.
 
  • #4
cool_dude said:
oops you i forgot the square. so then i get 26.8 seconds. does that make sense for a plane to take amount of time for lift of? i think it makes sense to me. not sure. also does this mean that we don't care about the required velocity for takeoff?

hmmm the second part is tricky. i thoght that t - 1 would mean that let's say it took 10 seconds then t = 10 and the second before it is t - 1 = 9. I'm a bit confused on this part.

Your time looks correct.

Suppose you know the distance traveled in the first 10 seconds... and the distance traveled in the first 9 seconds... you can get the distance in the last second by subtracting the two...
 
  • #5
Wow thanks for the fast reply. And thank you very much for all your help. i got both answers correct thanks to you. :)
 

1. How do airplanes stay on the runway during takeoff?

Airplanes have a high enough power-to-weight ratio that allows them to generate enough thrust to move forward on the runway. Additionally, the wings of the airplane are designed to create lift, keeping the plane on the ground during takeoff.

2. Why do airplanes sometimes have to wait on the runway before takeoff?

Airplanes may have to wait on the runway due to air traffic control instructions, weather conditions, or runway congestion. This is to ensure the safety of all planes in the air and on the ground.

3. What is the purpose of the markings on a runway?

The markings on a runway serve as visual aids for pilots during takeoff and landing. They indicate the length of the runway, the centerline, and other important information such as holding points and runway exits.

4. How do pilots know when to start their takeoff roll on the runway?

Pilots use a variety of instruments and calculations to determine the appropriate speed and distance needed for takeoff. They also receive instructions from air traffic control and follow specific procedures set by the airline.

5. Can an airplane land on any runway?

No, airplanes must land on runways that are long enough and strong enough to support their size and weight. Additionally, certain runways may be designated for specific types of aircraft or may have restrictions due to weather conditions or surrounding terrain.

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