Explanation Given: Equation of the curve in vector form is r ( θ ) = 〈 cos θ , sin 2 θ 〉 , θ = π 4 Formula used: Velocity, v ( θ ) = r ' ( θ ) Acceleration, a ( θ ) = r ' ' ( θ ) Tangent vector, T = v ∥ v ∥ Normal vector, N = a N N a N , where a N = ∥ a N N ∥ , a N N = a − a T T and a T = a . T Calculation: We have v ( θ ) = r ' ( θ ) = 〈 − sin θ , 2 cos 2 θ 〉 and a ( θ ) = r ' ' ( θ ) = 〈 − cos θ , − 4 sin 2 θ 〉 At θ = π 4 , v ( π 4 ) = 〈 − sin π 4 , 2 cos π 2 〉 = 〈 − 1 2 , 0 〉 and a ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14, Problem 33CRE

To determine

The acceleration vector a at the point indicated as a sum of tangential and normal components for $r (θ) = 〈 \cos θ, \sin 2 θ 〉, θ = \frac{π}{4}$ .

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Chapter 14, Problem 32CRE

Chapter 14, Problem 34CRE

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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The acceleration vector a at the point indicated as a sum of tangential and normal components for r ( θ ) = 〈 cos θ , sin 2 θ 〉 , θ = π 4 .

Solution Summary: The author explains the equation of the curve in vector form is r = cos, sin 2.

Concept explainers

The acceleration vector a at the point indicated as a sum of tangential and normal components for $r (θ) = 〈 \cos θ, \sin 2 θ 〉, θ = \frac{π}{4}$ .

Want to see the full answer?

Chapter 14 Solutions

The acceleration vector a at the point indicated as a sum of tangential and normal components for r ( θ ) = 〈 cos θ , sin 2 θ 〉 , θ = π 4 .

Solution Summary: The author explains the equation of the curve in vector form is r = cos, sin 2.

Concept explainers

The acceleration vector a at the point indicated as a sum of tangential and normal components for r(θ)=〈cosθ,sin2θ〉,θ=π4.

Want to see the full answer?

Chapter 14 Solutions

The acceleration vector a at the point indicated as a sum of tangential and normal components for $r (θ) = 〈 \cos θ, \sin 2 θ 〉, θ = \frac{π}{4}$ .