Airplane takeoff point of no return · BPhO 2009 #11
Physics · mechanics
Problem
A plane accelerates from rest to take off from a runway. There is a point of no return where the pilot will not be able to stop the plane before the end of the runway if he fails to take off. The runway is 2 km long and the plane can accelerate at 3 ms⁻² and can decelerate at 2 ms⁻². We can calculate the length of time available from the start of the take off to the point of no return.
a) Sketch a graph of the speed of the plane against time for the situation where the plane fails to take off but the whole length of the runway is used. (no values are required)
b) If t₁ is the time taken for the plane to reach its maximum speed v, and t₂ is the time taken for it to decelerate before it goes beyond the end of the runway, express v in terms of t₁ and t₂, and the respective accelerations.
c) Calculate the distance s₁ travelled by the plane whilst accelerating, in terms of t₁, and the distance s₂ travelled by the plane whilst decelerating, in terms of t₂.
d) From your answers to (b) and (c), calculate the value of t₁, the time taken to reach the point of no return, given that the runway is 2 km long.