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: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 14, Problem 33CRE

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14, Problem 32CRE

Chapter 14, Problem 34CRE

Students have asked these similar questions

Let r(t) (15, cos t, -3 sin t) be the position vector of an object. Find the velocity and speed of the object.

The figure shows an overhead view of a 0.026 kg lemon half and two of the three horizontal forces that act on it as it is ona frictionless table. Force F has a magnitude of 3 N and is at e, - 31. Force F2 has a magnitude of 10 N and is at 02- 33". In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity V (131-14) m/s, and (c) has the V = (12i – 14ij) m/s?, where t is time? %3D

Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ, cos θ, cos 3θ〉, θ = π/3

Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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 $r (θ) = 〈 \cos θ, \sin 2 θ 〉, θ = \frac{π}{4}$ .