![Precalculus Enhanced with Graphing Utilities](https://www.bartleby.com/isbn_cover_images/9780321795465/9780321795465_largeCoverImage.gif)
Projectile Motion The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations
See the illustration.
![Chapter 10.7, Problem 60AYU, Projectile Motion The position of a projectile fired with an initial velocity 0 feet per second and , example 1](https://content.bartleby.com/tbms-images/9780134119281/Chapter-10/images/19281-10.7-60ae-question-digital.jpg)
a. Obtain the rectangular equation of the trajectory and identify the curve.
b. Show that the projectile hits the ground when .
c. How far has the projectile traveled (horizontally) when it strikes the ground? In other words, find the range .
d. Find the time when . Then find the horizontal distance and the vertical distance traveled by the projectile in this time. Then compute . This is the distance , the range, that the projectile travels up a plane inclined at to the horizontal . See the following illustration. (See also Problem 99 in Section 7.6.)
![Chapter 10.7, Problem 60AYU, Projectile Motion The position of a projectile fired with an initial velocity 0 feet per second and , example 2](https://content.bartleby.com/tbms-images/9780134119281/Chapter-10/images/19281-10.7-60ae_1-question-digital.jpg)
![Check Mark](/static/check-mark.png)
To find:
a. The rectangular equation of the trajectory and identify the curve.
Answer to Problem 60AYU
a.
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
a. ,
is a quadratic function of and it represents the graph of a parabola where , and .
![Check Mark](/static/check-mark.png)
To find:
b. To show that the projectile hits the ground when .
Answer to Problem 60AYU
b.
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
b.
![Check Mark](/static/check-mark.png)
To find:
c. How far has the projectile traveled (horizontally) when it strikes the ground? In other words, find the range R.
Answer to Problem 60AYU
c.
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
c. To find R
We substitute in
![Check Mark](/static/check-mark.png)
To find:
d. Find the time when . Then find the horizontal distance and the vertical distance traveled by the projectile in this time. Then compute . This is the distance R, the range, that the projectile travels up a plane inclined at to the horizontal .
Answer to Problem 60AYU
d. as
Explanation of Solution
Given:
The position of a projectile fired with an initial velocity feet per second and at an angle to the horizontal at the end of seconds is given by the parametric equations.
,
Formula used:
,
Calculation:
d.
;
At
hence,
as
Chapter 10 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Calculus & Its Applications (14th Edition)
Precalculus (10th Edition)
University Calculus: Early Transcendentals (4th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- 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
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)