   Chapter 12.3, Problem 29E

Chapter
Section
Textbook Problem

# Projectile Motion In Exercises 25–38, use the model for projectile motion, assuming there is no air resistance.Eliminate the parameter t from the position vector for the motion of a projectile to show that the rectangular equation is y = − 16   sec 2 θ v 0 2 x 2 + ( tan   θ ) x + h .

To determine

To prove: The rectangular equation of projectile motion is y=16sec2θv02x2+(tanθ)x+h, if the parameter t is eliminated from the position vector.

Explanation

Proof:

The position vector of projectile motion is r(t)=(v0cosθ)ti+[h+(v0sinθ)t12gt2]j.

Now, consider above equation in parametric form, so

x=v0cosθt …… (1)

And,

y=h+(v0sinθ)t12gt2 …… (2)

Now, eliminate t from both x and y,

So, from equation (1),

t=xv0cosθ …… (3)

Now, put the value of t in equation (2),

y=h+(v0sinθ

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