   Chapter 10.3, Problem 60E

Chapter
Section
Textbook Problem

Path of a Projectile When the projectile in Exercise 59 is launched at an angle θ with the horizontal, its parametric equations are x = ( 90 cos θ ) t and y = ( 9 sin θ ) t − 16 t 2 . Find the angle that maximizes the range of the projectile. Use a graphing utility to find the angle that maximizes the arc length of the trajectory.

To determine

To calculate: The angle which maximises the range of the projectile with parametric equations, x=(90cosθ)t and y=(90sinθ)t16t2. And, by the use of the graphing utility find the angle which maximises the arc length.

Explanation

Given:

The parametric equations, x=(90cosθ)t and y=(90sinθ)t16t2.

Calculation:

Consider the parametric equations, x=(90cosθ)t and y=(90sinθ)t16t2.

To find the range for t, put y=0.

(90sinθ)t16t2=0t(90sinθ16t)=0t=0,9016sinθ

Now, put t=0 in the equation, x=(90cosθ)t. Therefore, x=0.

Discard x=0, as this will not provide any angle for θ.

Now, put t=9016sinθ in the equation, x=(90cosθ)t

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