To show: For a satellite following a curve that is a
The acceleration
Also, to show that the satellite is directed toward the origin and has magnitude inversely proportional to the square of the distance.
Answer to Problem 80E
It is shown that the acceleration vector is
Explanation of Solution
Given information:
The position vector of the satellite is given by:
Concept used:
For polar coordinates of a point
Here,
and
Where,
Differentiate x with respect to t .
Differentiate y with respect to t .
Now differentiate
Thus, the acceleration vector will be :
Using the fact
Here
Thus,
It implies
Since the position vector
It implies that the acceleration vector of the satellite is directed toward the origin.
The magnitude of the acceleration vector of the satellite is given by:
Here,
Thus, the magnitude of the acceleration vector of the satellite is inversely proportional to the square of the distance of the satellite from the origin.
Chapter 10 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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