Chapter 10.1, Problem 20ES

(a) Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for $t\ge 0$ are $x=t-2\sin t,y=3-2\cos t$

(b) Assuming that the plane flies in a room in which the floor is at $y=0,$ explain why the plane will not crash into the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.]

(c) How high must the ceiling be to ensure that the plane does not touch or crash into it?