Parametric equations for a Particle Path
Not what you're looking for?
Find the parametric equations for the path of a particle that moves along the circle
x^2 + (y-1)^2 = 4
as follows:
(a) Once around clockwise, starting at (2,1);
(b) Three times around counterclockwise, starting at (2,1);
(c) Halfway around counterclockwise, starting at (0,3).
Purchase this Solution
Solution Summary
The expert examines parametric equation for a particle path.
Solution Preview
Please see the attached file.
Any two dimensional simple curve can be described as a parametric equation of the parameter t
(1.1)
The general Cartesian equation of a circle of radius R centered around is:
(1.2)
This equation simply tells us that the circle is formed by the set of points that are equally distant from the point , and that distance is R.
If we set and , we get an origin-centered unit circle:
(1.3)
It is easy to see that its parametric equations are:
(1.4)
Where t is the angle measured counterclockwise from the positive x-axis.
If we want to "inflate" the unit circle to radius R, all we have to do is to multiply the x and y coordinates ...
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts