I am trying to find the unit tangent vector T(t)
Heres the problem
\(\displaystyle r(t) = ti + \frac{1}{t}j, t = 1\)
\(\displaystyle v(t) = i - \frac {1}{t^2} j\)
then
\(\displaystyle a(t) = \frac {2}{t^3} j\)
I think the magnitude is:
\(\displaystyle ||v(t)|| = \sqrt \frac{2} {t^4} j\)
then the solutions manual has this:
\(\displaystyle T(t) = \frac {v(t)}{ || v(t) ||} = \frac{t^2} {\sqrt{ t^4 + 1}} (i - \frac{ 1}{t^2}j )\)
I am not sure how they are getting this.
Can someone help me with the steps? I would appreciate this!!
Heres the problem
\(\displaystyle r(t) = ti + \frac{1}{t}j, t = 1\)
\(\displaystyle v(t) = i - \frac {1}{t^2} j\)
then
\(\displaystyle a(t) = \frac {2}{t^3} j\)
I think the magnitude is:
\(\displaystyle ||v(t)|| = \sqrt \frac{2} {t^4} j\)
then the solutions manual has this:
\(\displaystyle T(t) = \frac {v(t)}{ || v(t) ||} = \frac{t^2} {\sqrt{ t^4 + 1}} (i - \frac{ 1}{t^2}j )\)
I am not sure how they are getting this.
Can someone help me with the steps? I would appreciate this!!
