Determine the unit tangent vector

chwala
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Homework Statement
see attached
Relevant Equations
vector differentiation
1644910436015.png


I need a justification that ##|\dfrac {dr}{dt}|##=##\dfrac {ds}{dt}## cheers guys... all the other steps are easy and clear to me...
 
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chwala said:
Homework Statement:: see attached
Relevant Equations:: vector differentiation

View attachment 297138

I need a justification that [Modulus ##\big | \dfrac {dr}{dt} \big |##=##\dfrac {ds}{dt}##] cheers guys... all the other steps are easy and clear to me...
We have ##ds \equiv |d\vec r|##.
 
Aaaaah Perok cheers!
PeroK said:
We have ##ds \equiv |d\vec r|##.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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