Can you help me with this one 71 Find the tan gential Component a Tand the nor mal component a Nfd accelerationa f r Ct) = (2+?, 7+3>fincrion of tasaa T Ct2 :%3DaN(t)=

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Description: Can you help me with this one 71 Find the tan gential Component a Tand the nor mal component a Nfd accelerationa f r Ct) = (2+?, 7+3>fincrion of tasaa T Ct2 :%3DaN(t)=

Answered: 71 Find the tan gential. Component aT…

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71 Find the tan gential. Component aT and the normal componenteN O e accekration a funcrion of t. if +Ct) = (2+2, 7+3> %3D as a T Ct) : %3D a N (t)=

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 80E

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Question

Can you help me with this one

71 Find the tan gential Component a T
and the nor mal component a N
fd acceleration
a f r Ct) = (2+?, 7+3>
fincrion of t
as
a
a T Ct2 :
%3D
aN
(t)=

Expert Solution

Step 1

Given

$r (t) = <2 t^{2}, 7 t^{3}> r' (t) = <4 t, 21 t^{2}> r'' (t) = <4, 42 t>$

Tangential component of acceleration vector is

$a_{T} = \frac{r' (t) . r'' (t)}{|r' (t)|} = \frac{4 t (4) + 21 t^{2} (42 t)}{\sqrt{{(4 t)}^{2} + {(21 t^{2})}^{2}}} = \frac{882 t^{3} + 16 t}{t \sqrt{16 + 441 t^{2}}} = \frac{882 t^{2} + 16}{\sqrt{16 + 441 t^{2}}}$

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