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1. Given r(t) = 2 cos t i + 2 sintj+ 10tk; 0

1. Given r(t) = 2 cos t i + 2 sintj+ 10tk; 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
1. Given r(t) = 2 cos t i + 2 sin tj+ 10tk; 0 <t< 2n , find the tangential and normal components of acceleration. Then find a at t = 2*
Transcribed Image Text:1. Given r(t) = 2 cos t i + 2 sin tj+ 10tk; 0 <t< 2n , find the tangential and normal components of acceleration. Then find a at t = 2*
Expert Solution
Step 1

Given that rt=2cost i+2dint j+10t k where 0≤t≤2π.

It is required to find the tangential and normal components of acceleration.

It is known that the tangential and normal components of acceleration is given by

 aT=a→·T=v·a→vaN=a→·N=v×a→v=a→2-aT2

Also these components are related by the formula,

a→t=aTT+aNN

Where T and N is unit tangent and normal vector.

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