Concept explainers
Interpretation:
The analytical solution for
Concept Introduction:
The limiting velocity of an object is called its terminal velocity. It is obtained by finding the limit of
The fixed point of the differential equation in terms of
Answer to Problem 13E
Solution:
a)
b)
c)
d)
e)
Explanation of Solution
a) The differential equation which shows the velocity
Integrating with respect to t gives
We are given that
Where
Therefore, the analytical solution for
b) The terminal velocity of the sky diver can be calculated as
Thus, the terminal velocity of the sky diver is
c) The fixed point of the
The fixed is obtained by putting
Thus, the terminal velocity of the sky diver is
d) The average velocity of the sky diver can be calculated as
e) We can find the distance fallen s from the equation for v(t) as
After substitution equation (1) becomes
But
But terminal velocity is
Therefore,
After substituting the given values we can write
After solving it we get
The drag constant k can be calculated as
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Chapter 2 Solutions
Nonlinear Dynamics and Chaos
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning