Chapter 12.3, Problem 31E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Projectile Motion In Exercises 27-40, use the model for projectile motion, assuming there is no air resistance and g = 32 feet per second per second. 31. Eliminate the parameter t from the position vector for the motion of a projectile to show that the rectangular equation is y = − g sec 2 θ 2 v p 2 x 2 + ( tan θ ) x + h

To determine

To prove: The motion of a projectile of the rectangular equation is,

y=gsec2θ2v02x2+(tanθ)x+h.

Explanation

Given:

The motion of projectile is y=âˆ’gsec2Î¸2v02x2+(tanÎ¸)x+h.

Proof:

Neglecting air resistance, the path of a projectile launched from an initial height h with initial speed v0 at an angle of elevation Î¸? is described by the vector function,

r(t)=(v0cosÎ¸)ti+[h+(v0sinÎ¸)tâˆ’12gt2]j â€¦...â€¦... (1)

The rectangular coordinates are,

r(t)=xi+yj â€¦...â€¦..

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