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Motion with Constant Acceleration problem

  • #1

Homework Statement


A smaller propeller airplane can comfortably achieve a high enough speed to take off on a runway that is 1/4 mile long. A large, fully loaded passenger jet has about the same acceleration from rest, but needs to achieve twice the speed to take off. What is the minimum runway length that will serve?

Hint: you can solve this problem using ratios without having any additional information.


Homework Equations



I used Vf^2=Vi^2 + 2a(x)

The Attempt at a Solution



Vf^2=Vi^2 + 2a(x)
Vi=0
Vf^2 = 2a(.25)
.25 = Vf^2/2a

now how do i solve for the larger plane?
 

Answers and Replies

  • #2
berkeman
Mentor
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Homework Statement


A smaller propeller airplane can comfortably achieve a high enough speed to take off on a runway that is 1/4 mile long. A large, fully loaded passenger jet has about the same acceleration from rest, but needs to achieve twice the speed to take off. What is the minimum runway length that will serve?

Hint: you can solve this problem using ratios without having any additional information.


Homework Equations



I used Vf^2=Vi^2 + 2a(x)

The Attempt at a Solution



Vf^2=Vi^2 + 2a(x)
Vi=0
Vf^2 = 2a(.25)
.25 = Vf^2/2a

now how do i solve for the larger plane?
Welcome to the PF.

Be sure to carry units along in your equations as you work. It helps to avoid mistakes in unit conversions, and helps to make the equations clearer. It took me a beat or two to figure out that the 0.25 was in miles.... :smile:

Now, you have an equation for the motion of the small plane, with its final velocity Vf and the distance it takes to take off (0.25 miles). The larger plane requires twice the final velocity to take off, but has the same acceleration. Write a similar equation for the large plane with the distance as a variable, and use the hint from the problem about taking ratios to solve for the unknown...
 

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