Concept explainers
The rate of the removal.
Answer to Problem 8P
The dog never catches the rabbit.
Explanation of Solution
Given information:
Snow began to fall during the morning of February 2 and continued steadily into the afternoon. At noon a snow plow began removing snow from a road at a constant rate. The plow traveled 6 km from noon to 1 PM out only 3 km from 1 PM to 2 PM. When did the snow begin to fall?
Formula used:
Calculation:
The distance travelled by the dog from point (L, 0) to (0, s) is given by the following equation.
The speed of the dog is twice the speed of the rabbit it means position of the rabbit when dog has travelled the distance s is
Here the dog runs in a Straight line to catch the rabbit, so the rate of change of y with respect to x is the slope of the line joining the points
Equate the expressions for
Hence the desired differential equation is
Solve the differential equation
Let
Now put these values in the differential equation
This equation can be solved by separating the variables and then by integrating it
When
Put
Now solve this equation for Z.
Since,
Now solve these equations one by one separately.
Here
So,
Put this value into the equation
Hence the solution to the differential equation
Solve the second equation
It can be rewritten as
Hence solution to equation will be
Here
Put this value into the equation
Hence the solution to the differential equation
Evaluate the
Use either of the equations
Hence dog catches the rabbit at distance of
The distance travelled by the dog from point (L, 0) to (0, 5) is given by the following equation.
The speed of the dog is half the speed of the rabbit it means position of the rabbit when dog has travelled the distance sis (0,2s).
Here the dog runs in a straight line to catch the rabbit, so the rate of change of y with respect to x is the slope of the line joining the points (0, 2s), (x, y).
Equate the expressions for
Hence the desired differential equation is
Solve the differential equation
Let
Now put these values in the differential equation
This equation can be solved by separating the variables and then by integrating it
When
Put
Now solve this equation for Z.
Since,
Here
So
Hence the solution to the differential equation
Evaluate the limit
Use the equation
Hence dog never catches the rabbit.
Conclusion:
The dog never catches the rabbit.
Chapter 7 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning