11_Proj_T_arclen

11_Proj_T_arclen - Review of Projectiles ex ex ex Unit...

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Unformatted text preview: Review of Projectiles ex. ex. ex. Unit Tangent Vector T (t) ex. r = e it Find T(t). ( t ,s . t ) , n 3 t Arclength (s) d x d y d z s + + d = t t t d 1 d t d t t 2 2 2 2 where x, g h == ( f y, t ( (= t ) t ) ) z . Since 2 2 2 x y z d d d v = + + t t t d d d , s vd = t t 2 t 1 . ex. Find the length of r 2 + 03 ( +, , t ) t 1 t. =t 3 , t ex. Do: A particle travels along the path (1 ) 0 ,, ? How far has it traveled from P(0, 1, 0) to Q 6 r= t s3 ( s, t t t i c, . ) n o Unit Normal vector r r T N= r T Since T has length 1, ex. r s,o t Find N ( i c3 t ns . ) t t = , . Find TN . Curvature Curvature, , measures how sharply a curve bends. We want some way of measuring this. We will look at the tangent vectors. Use the unit tangent vectors to keep uniform lengths so that we only compare the change in direction. is the magnitude of the rate of change of T arclength of the curve. with respect to the d T d T d = T t = = d s d s v d t ex. Find for r= s s . ( ata t c i ) o n , t ...
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11_Proj_T_arclen - Review of Projectiles ex ex ex Unit...

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