DYNAMICS  CASE STUDY



Introduction

Top View of Plane Motion


After dropping a relief package, a plane reverses direction and heads for home. The pilot wants to increase the speed, but he is not sure what the acceleration will do to the plane.
What is known:
 The plane begins the semicircular turn (t = 0) with an initial velocity of 176 ft/s.
 The path of the plane remains horizontal.
 The pilot increases the speed of the plane along the flight path at a rate of
a_{t} = 2 + 1.5 t ft/s^{2} (tangent to path)




Plane Path and Boundary Conditions


Question


If it takes 16 seconds to complete the turn,
 what is the speed of the plane at the end of the turn (point B)?
 and what is the maximum centripetal acceleration that the plane
experiences during the turn? How does it compare to gravitational acceleration?





Approach



 Because the specified acceleration is tangent to the path of the plane,
it is better to analyze the motion using normal and tangential coordinates.
 Use the tangential component of the plane's acceleration to determine
the speed at B.
 Use the normal component of the acceleration to determine the maximum
centripetal acceleration.



