Chapter 13, Problem 11PS

(a)

To determine

To calculate: For a given projectile, launched at an angle of $45°$ with the horizontal.

Initial velocity is $64\text{ feet per sec}$, find the parametric equations for the path of the projectile in terms of the parameter t

representing time.

(b)

To determine

To calculate: The projectile is launched at an angle of $45°$ with the horizontal. The initial velocity is $64\text{ feet per sec}$ is given, find the angle $\alpha$ that the camera makes with the horizontal in terms of $x\text{ and }y$ and interms of $t$.

(c)

To determine

To calculate: The equation is $\alpha ={\tan }^{-1}\left(\frac{32\sqrt{2}t-16t^2}{32\sqrt{2}t+50}\right)$ is given, find the value of $\frac{d\alpha }{dt}$.

(d)

To determine

To graph: The provided equation is $\alpha ={\tan }^{-1}\left(\frac{32\sqrt{2}t-16t^2}{32\sqrt{2}t+50}\right)$, graph the provided 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.

(e)

To determine

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