To prove: That the particle’s velocity is always orthogonal to both its position and its acceleration.
Explanation of Solution
Given information:
The position
Calculation:
The given position vector is
Consider the position vector be
It is known that the first derivative of
So,
Write the acceleration vector as:
The slope of the velocity vector is the negative reciprocal of the slopes of the position vector and the acceleration vector.
Here, the slope of the position vector is
The slope of the velocity vector is
The slope of the acceleration vector is
This means that the velocity is orthogonal to the position and the acceleration.
Hence, the statement is proved.
Chapter 11 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus & Its Applications (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus and Its Applications (11th Edition)
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