Question

You have just landed your first job as a structural engineer and you have been asked to design a regional airport for small planes. Your manager informs you that the planes that will use this runaway must reach a speed before takeoff of at least 28.1 m/s, and can accelerate at 2 m/s2. What is the minimum length your runaway must have to facilitate a safe take off

Answer 1

Answer: $197.40\ m$

Explanation:

Given

final velocity at takeoff $v=28.1\ m/s$

Acceleration of the plane can be $a=2\ m/s^2$

Initial velocity is zero for the plane i.e. $u=0$

Using the equation of motion

$\Rightarrow v^2-u^2=2as\quad [\text{s=displacement}]\\\text{Insert the values}\\\Rightarrow (28.1)^2-0=2\times 2\times s\\\\\Rightarrow s=\dfrac{789.61}{4}\\\\\Rightarrow s=197.40\ m$

Thu,s the minimum length must be $197.40\ m$