- #1
BennyT
- 21
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Homework Statement
[/B]This problem is from Jon Rogawski's Calculus-Early Transcendentals
At a certain moment, a moving particle has velocity v={2,2,-1} and a={0,4,3}. Find T, N and the decomposition of a into tangential and normal components.
Homework Equations
ANYTHING IN [ ] REPRESENTS A LENGTH OF A QUANTITY and . stands for dot product
T[/B](t)=v(t)/[v(t)]
N(t)=T '(t)/[T '(t)]
an=√([a]^2-at^2)
at=a.T
an=a.N=√([a]^2-at^2)
The Attempt at a Solution
So I'm trying to find an, the normal component of acceleration, but by using the two definitions and equations found in the book I am coming to different values. So I first calculated T={2/3,2/3,-1/3}, and then N={0,4/5,3/5}. Then I calculated at=5/3 and then I calculated an by the first equation (an=√([a]^2-at^2)) to equal an=(10/3)(√2), but using the second equation I get an=5. What am I doing wrong? And also, do T and N always have to be orthogonal? This isn't a graded assignment or anything, but it's causing me frustration. Thanks for your time.