Textbook Problem

Projectile Motion A projectile is launched with an initial velocity of 120 feet per second at a height of 5 feet and at an angle of ${30}^{\circ }$ with the horizontal.

(a) Determine the vector-valued function for the path of the projectile.

(b) Use a graphing utility to graph the path and approximate the maximum height and range of the projectile.

(c) Find $v(t),\Vert v(t)\Vert$, and a(t).

(d) Use a graphing utility to complete the table.

t	0.5	1.0	1.5	2.0	2.5	3.0
Speed

(e) Use a graphing utility to graph the scalar functions $a_T$ and $a_N$. How is the speed of the projectile changing when $a_T$ and $a_N$ have opposite signs?