Chapter 13, Problem 11PS

(a)

To determine

To calculate: The parametric equations for the path of the projectile in terms of the parameter t

representing time if Projectile is launched at an angle of $45°$ with the horizontal.

Initial velocity is $64\text{ feet per sec}$.

The figure is:

(b)

To determine

To calculate: The angle $\alpha$ that the camera makes with the horizontal in terms of $x\text{ and }y$ and in terms of $t$ if A television camera is located in the plane of the path of the projectile $50\text{ feet}$ behind the launch site and

(c)

To determine

To calculate: The value of $\frac{d\alpha }{dt}$ if $\alpha ={\tan }^{-1}\left(\frac{32\sqrt{2}t-16t^2}{32\sqrt{2}t+50}\right)$

(d)

To determine

To graph: The equation of $\alpha$ in terms of t and find out if the graph is symmetric to the axis of parabolic arch of the projectile and also determine the time at which the rate of change of $\alpha$ is greatest if $\alpha ={\tan }^{-1}\left(\frac{32\sqrt{2}t-16t^2}{32\sqrt{2}t+50}\right)$

(e)

To determine

To calculate: The time at which the angle $\alpha$ is maximum and also find out if this occur when the projectile is at its greatest height if $\alpha ={\tan }^{-1}\left(\frac{32\sqrt{2}t-16t^2}{32\sqrt{2}t+50}\right)$