The speed of the ball at which it should be thrown upward to reach a maximum height of
Answer to Problem 112E
The speed of the ball at which it should be thrown upward to reach a maximum height of
Explanation of Solution
Given:
An object thrown or fired straight upward at an initial speed of
Result used:
Discriminant of a
The quantity
1. If
2. If
3. If
Calculation:
Substitute
Compare this equation with the general form
Here
Note that, the ball will reach the highest point only once and the quadratic equation has only one solution when the discriminant is zero.
Therefore, let the discriminant be zero.
On further simplifications, the following is obtained.
Since the speed should be always positive, the value of
Thus, the speed of the ball at which it should be thrown upward to reach a maximum height of
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th 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