Concept explainers
(a)
To calculate: The velocity
(a)
Answer to Problem 48E
The required velocity is
Explanation of Solution
Given information:
The position of the particle:
Calculation:
The given position of the particle is
It is known that for a position vector
So,
Now,
Hence, the required velocity is
(b)
To determine: The values of t for which the particle is at rest.
(b)
Answer to Problem 48E
The required values of t are
Explanation of Solution
Given information:
The position of the particle:
Calculation:
The given position of the particle is
It is known that for a position vector
So,
Now,
Thus, the required velocity is
It is seen that the particle is at rest at
This means,
For
Also, for
Hence, the required values of t are
(c)
To write: The equation for the path of the particle in terms of x and y that does not involve trigonometric functions.
(c)
Answer to Problem 48E
The required equation is
Explanation of Solution
Given information:
The position of the particle:
Calculation:
The given position of the particle is
To write an equation for the path of the particle, use the formula
The equation can be written as:
Hence, the required equation is
(d)
To graph: The path of the particle.
(d)
Explanation of Solution
Given information:
The position of the particle:
Calculation:
The given position of the particle is
The required for the path of the particle is shown below:
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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