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Calculus and Beyond Homework Help
Finding unit normal vectors and normal/tangent components of accelerat
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[QUOTE="icesalmon, post: 4514959, member: 302121"] [h2]Homework Statement [/h2] given r(t) = <t, 1/t,0> find T(t) N(t) a[SUB]T[/SUB] and a[SUB]N[/SUB] at t = 1 [h2]Homework Equations[/h2] T(t) = r'/||r'|| N(t) = T'/||T'|| a[SUB]T[/SUB] = a . T = (v . a)/||T|| a[SUB]N[/SUB] = a . N = ||v x a||/||v|| = sqrt(||a||[SUP]2[/SUP] - a[SUB]T[/SUB][SUP]2[/SUP]) [h2]The Attempt at a Solution[/h2] for my T(t) I get <t[SUP]2[/SUP], -1 , 0>/(sqrt(1+t[SUP]4[/SUP]) (I like keeping things in 3 dimensions even if there is no contribution in the z direction) and I am not calculating the normal vector if there isn't some algebra I can use to simplify this greatly , which I am not seeing, t[SUP]4[/SUP] + 1 I don't believe I can factor and I can't think of any other way to simplify this one so I'm just moving around through the problem set looking for some r(t) = <cost, sint, t> type of vector that I can simply differentiate and use identities with, desperately trying to avoid those other problems [/QUOTE]
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Homework Help
Calculus and Beyond Homework Help
Finding unit normal vectors and normal/tangent components of accelerat
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