Explanation Proof: Consider the provided parametric equations, x = ( v 0 cos θ ) t ...... ( 1 ) And y = h + ( v 0 sin θ ) t − 16 t 2 ...... ( 2 ) Now, first eliminate the parameter t in the parametric equations. Take equation (1), x = ( v 0 cos θ ) t t = x v 0 cos θ Substitute the value of t in equation (2) y = h + ( v 0 sin θ ) t − 16 t 2 = h + ( v 0 sin θ ) ( x v 0 cos θ ) − 16 ( x v 0 cos θ ) 2 = h + ( tan θ ) x &

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Author: Ron Larson

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Chapter 6.6, Problem 96E

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To prove: The rectangular equation is y=−16sec2θv02x2+(tanθ)x+h for the parametric equation x=(v0cosθ)t and y=h+(v0sinθ)t−16t2 for the motion of a projectile by eliminating the variable t.

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Chapter 6.6, Problem 95E

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To prove: The rectangular equation is y = − 16 sec 2 θ v 0 2 x 2 + ( tan θ ) x + h for the parametric equation x = ( v 0 cos θ ) t and y = h + ( v 0 sin θ ) t − 16 t 2 for the motion of a projectile by eliminating the variable t .

Solution Summary: The author explains how to eliminate the parameter t in the parametric equations.

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To prove: The rectangular equation is y=−16sec2θv02x2+(tanθ)x+h for the parametric equation x=(v0cosθ)t and y=h+(v0sinθ)t−16t2 for the motion of a projectile by eliminating the variable t.

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