   Chapter 10.3, Problem 55E

Chapter
Section
Textbook Problem

# Path of a Projectile The path of a projectile is modeled by the parametric equations x = ( 90 cos 30 ∘ ) t   and   y = ( 90 sin 30 ∘ ) t − 16 t 2 where x and y are measured in feet.(a) Use a graphing utility to graph the path of the projectile.(b) Use a graphing utility to approximate the range of the projectile.(c) Use the integration capabilities of a graphing utility to approximate the arc length of the path. Compare this result with the range of the projectile.

(a)

To determine

To-graph: The path of the projectile which is given by the parametric equations, x=(90cos30°)t and y=(90sin30°)t16t2.

Explanation

Given:

The parametric equations, x=(90cos30°)t and y=(90sin30°)t16t2.

Graph:

Consider the equations, x=(90cos30°

(b)

To determine

To-determine: The range of the projectile in part (a) by the graphing utility.

(c)

To determine

To-calculate: The approximate arc length of the path in part (a) by the use of graphing utility. Also, compare the result with the range of the projectile.

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