Concept explainers
Artillery A projectile fired into the first quadrant from the origin of a
(a) What angle of elevation did he use?
(b) If the angle of elevation is also given by , where is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
a. The angle of elevation used by the artillery man to hit the projectile on the enemy bunker.
Answer to Problem 81AYU
Solution:
The angle of elevation used by the artillery man to hit the projectile on the enemy bunker.
Explanation of Solution
Given:
The height of the enemy bunker .
Horizontal location of the enemy bunker from the projectile artillery man .
Time taken for the projectile to hit the enemy bunker .
acceleration due to gravity .
Formula used:
angle of elevation of the launcher.
Horizontal location of the enemy bunker from the projectile artillery man (Launcher).
The height of the enemy bunker.
Time taken for the projectile to hit the enemy bunker.
acceleration due to gravity.
Calculation:
To find , we need to find because has the same range as except where undefined.
Equation of the circle .
Where .
Both and are positive, therefore lies in the I quadrant.
Using the formula,
b.The muzzle velocity of the artillery piece.
Answer to Problem 81AYU
Solution:
The muzzle velocity of the artillery piece .
Explanation of Solution
Given:
Horizontal location of the enemy bunker from the projectile artillery man .
Time taken for the projectile to hit the enemy bunker .
From 81 (a),
Angle of elevation .
Formula used:
Where .
Calculation:
Using the formula,
Chapter 7 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Glencoe Math Accelerated, Student Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
Thomas' Calculus: Early Transcendentals (14th 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