Answered: Suppose r'(t) has units of m/s. Explain…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units) and carries information only about direction.

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Suppose r'(t) has units of m/s.

To explain why $Let r(t) be a differential vector valued function Now we look for the derivative r'(t) The vector r'(t) points in the direction of travel and its length tells us the speed of travel Now we if we are interested in finding the direction of r' but not its length The standard unit tangent vector denoted by T(t) is given by: T (t) = \frac{r' (t)}{|r' (t)|}$ is dimensionless (has no units) and carries information only about direction.

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