(a)
The solution for
(a)
Answer to Problem 12.1P
The solution for
Explanation of Solution
Given nonlinear first-order equation,
Separating same variables in one side of the equation
Integrate the above equation and solving
Here,
Squaring on both sides
Let,
Conclusion:
Therefore, the solution for
(b)
Show that there is another solution for
(b)
Answer to Problem 12.1P
The another solution for
Explanation of Solution
Assume
Substitute
Since,
Conclusion:
The another solution for
(c)
Show that although
(c)
Answer to Problem 12.1P
It is shown that
Explanation of Solution
From part (a), the solution for
Now, consider
Substitute
Differentiate the above equation with respect to
Now, substitute
Substitute the above equation in
Thus,
From part (b), the solution for
Now, consider
Substitute
Differentiate the above equation with respect to
Now, substitute
Substitute the above equation in
Thus,
Now, consider
Substitute
Differentiate the above equation with respect to
Now, substitute
Substitute the above equation in
Thus,
Conclusion:
It is shown that
Want to see more full solutions like this?
- A shot putter releases a shot at 13 m/s at an angle of 42 degrees to the horizontal and from a height of 1.83 m above the ground. Calculate. Note: For each question draw a diagram to show the vector/s. Show all the steps and provide units in the answers. Provide answer to 2 decimal places unless stated otherwise. Answer all parts and show all work please.arrow_forwardA player kicks a football at the start of the game. After a 4 second flight, the ball touches the ground 50 m from the kicking tee. Assume air resistance is negligible and the take-off and landing height are the same (i.e., time to peak = time to fall = ½ total flight time). Calculate: Note: For each question draw a diagram to show the vector/s. Show all the step and provide units in the answers. Provide answer to 2 decimal places unless stated otherwise.)arrow_forwardIf I stand next to a wall on a frictionless skateboard and push the wall with a force of 25 N, what would my acceleration be if my mass is 75 kg?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON