Plane Landing on Tropical Island: Max Acceleration

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Homework Help Overview

The discussion revolves around a physics problem involving a plane landing on a small tropical island with a limited runway of 66 meters. The initial speed of the plane is given as 58 m/s, and participants are tasked with determining the maximum acceleration during landing, assuming constant acceleration.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the appropriate formulas to use for calculating acceleration and stopping distance, with some referencing the kinematic equation v^2 = Vo^2 + 2a(x-Xo). Questions arise about the meaning of variables, particularly the final velocity (V) when the plane comes to a stop.

Discussion Status

There is an ongoing exploration of different kinematic equations and their applicability to the problem. Some participants have provided guidance on interpreting the final velocity as zero when the plane lands, while others are clarifying the relationship between acceleration and distance during deceleration.

Contextual Notes

Participants are navigating through assumptions about the motion of the plane, including the implications of negative acceleration and the direction of motion. There is also a follow-up discussion about a related car acceleration and braking scenario, which introduces additional complexity to the conversation.

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A plane landing on a small tropical island has
just 66 m of runway on which to stop.
If its intial speed is 58 m/s, what is the
maximum acceleration of the plane during
landing, assuming it to be constant? Answer
in units of m/s^2.

i know I am supposed to use the equation v^2 = Vo^2 + 2a(x-Xo) but wht is V^2
 
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What formula would you have to use??

Daniel.
 
dextercioby said:
What formula would you have to use??

Daniel.


v^2 = Vo^2 + 2a(x-Xo) but wht is V^2
 
Well,the plane has to stop,so the final velocity should be...??

Daniel.
 
dextercioby said:
Well,the plane has to stop,so the final velocity should be...??

Daniel.


ah ha, ok i understand
 
follow up question

How long does it take for the plane to stop
with this acceleration? Answer in units of s.

i used the equation X = Xo + volt + 1/2at^2 is this correct?
 
How about
[tex]v_{fin}=v_{init}+at[/tex]

?? :wink:

The one u posted is correct as well,but te one suggested by me is more direct.

Daniel.
 
dextercioby said:
How about
[tex]v_{fin}=v_{init}+at[/tex]

?? :wink:

The one u posted is correct as well,but te one suggested by me is more direct.

Daniel.


i just got that
 
one more question

A car starts from rest and travels for 6.4 s with
a uniform acceleration of 3.3 m/s^2. The driver
then applies the brakes, causing a uniform
acceleration of 1.5 m/s^2.
If the brakes are applied for 2.5 s, how fast
is the car going at the end of the braking
period? Answer in units of m/s.

this is what I did, i subtracted the final acceleration from the initial and the the time for braking from the total time the car was traveling. then i used the equation V = Vo + at is that what you would do?
 
  • #10
No,i would compute the velocity after 6.4 secs and then the final velocity.Do the same & it'll be okay.

Daniel.
 
  • #11
one final add on

same question, How far has it gone? Answer in units of m.

i used the formula X = Xo + volt + 1/2at^2 for each time and acceleration then i subtracted the distance i got from the deceleration from the the distance i got for the acceleration
 
  • #12
Why did u subtract them...?It doesn't go backwards... :rolleyes: :wink:

Daniel.
 
  • #13
dextercioby said:
Why did u subtract them...?It doesn't go backwards... :rolleyes: :wink:

Daniel.

because one answer was negative even though distance cannot be negative( the decleration distance) and the acceleration distance was positive. am i supposed to add them?
 
  • #14
Of course,it decelerates in the same direction as it was accelerating (the velocity vector keeps direction,just the modulus varies),so they have to be added.

Daniel.
 
  • #15
dextercioby said:
Of course,it decelerates in the same direction as it was accelerating (the velocity vector keeps direction,just the modulus varies),so they have to be added.

Daniel.


im getting 72.27meters, can u check that for me? i think its wrong
 
Last edited:
  • #16
Nope,should be roughly 110m...


Daniel.
 
  • #17
plane on island

Vf^2 = Vi^2 + 2ad

Vf = 0. because the plane will be at stopped after it lands

rearrange formula

-Vi^ = 2ad

a = (-Vi^2)/(2*d)

a = (-58^2)/(2*66)

a = -25.5 m/s^2

aceleration is negative because the plane is slowing down while it lands.
 
  • #18
v2 is zero, once the plane lands it dosent have a velocity now does it
 

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