91Ó°ÊÓ

At the circus, a "human cannon ball" is shot from a large cannon with an initial velocity of \(90 \mathrm{ft} / \mathrm{sec}\) at an angle of \(65^{\circ}\) from the horizontal. How high is the acrobat after 1.2 sec? How long until the acrobat is again at this same height?

Use the equations for the horizontal and vertical components of the projected object's position to obtain the equation of trajectory \(y=(\tan \theta) x-\frac{16}{v^{2} \cos ^{2} \theta} x^{2} .\) This is a quadratic equation in \(x .\) What can you say about its graph? Include comments about the concavity, \(x\) -intercepts, maximum height, and so on.