Abu Butt April 10, 2014
MAT 1475H

Title: Where should a pilot start descent?
Abstract: In our project, we are trying to find out where should a pilot start to land/ descent. The pilot will start at a certain height. Our goal is to find out the speed, height, and length of the runway, from where an airplane should start landing. We will use knowledge of calculus to solve this problem.
 Introduction: The cruising Altitude is h when descent starts at a horizontal distance l from touching down at the origin.
 The pilot must maintain a constant horizontal speed v throughout descent.
 The absolute value of the vertical acceleration should not exceed a constant k ( which is much less than the acceleration due to gravity)

 Take the derivative of the equation P(x)=ax3+bx2 with respect to time (t)
 (dx/dt) being with respect to time, replace (dx/dt) with (-v). Where (-v) stands the horizontal velocity
 Find the derivative again
 Substitute a, and b that were found in the previous problem
 SOLVE