In Exercises 63 and 64, consider a projectile launched at a height of h feet above the

Chapter 10, Problem 64

(choose chapter or problem)

Projectile Motion   In Exercises 63 and 64, consider a projectile launched at a height of h feet above the ground at an angle of \(\theta\) with the horizontal. The initial velocity is \(v_0\) feet per second, and the path of the projectile is modeled by the parametric equations

\(x=\left(v_{0} \cos \theta\right) t\) and \(y=h+\left(v_{0} \sin \theta\right) t-16 t^{2}\).

An archer releases an arrow from a bow at a point 5 feet above the ground. The arrow leaves the bow at an angle of \(15^\circ\) with the horizontal and at an initial speed of 225 feet per second.

(a) Write a set of parametric equations that model the path of the arrow.

(b) Assuming the ground is level, find the distance the arrow travels before it hits the ground. (Ignore air resistance.)

(c) Use a graphing utility to graph the path of the arrow and approximate its maximum height.

(d) Find the total time the arrow is in the air.

Text Transcription:

theta

v_0

x=(v_0 cos theta) t

y=h+(v_0 sin theta) t-16t^2

15^p