Chapter 13, Problem 11PS

Projectile MotionA projectile is launched at an angle of 45°ï¿½ with the horizontal and with an initial velocity of 64 feet per second. A television camera is located in the plane of the path of the projectile 50 feet behind the launch site (see figure).

(a) Find parametric equations for the path of the projectile in terms of the parameter $t$ representing time.

(b) Write the angle αa that the camera makes with the horizontal in terms of $x$ and $y$ and in terms of $t$.

(c) Use the results of part (b) to find $\frac{d\alpha }{dt}.$

(d) Use a graphing utility to graph $\alpha$ in terms of $t$. Is the graph symmetric to the axis of the parabolic arch of the projectile? At what time is the rate of change of $\alpha$ greatest?

(e) At what time is the angle $\alpha$ maximum? Does this occur when the projectileis at its greatest height?