Concept explainers
a.
To find: The function with height
Given information:
The ball through upward at height 5 feet with vertical velocity of 50 feet per second.
Calculations:
The path of ball is parabolic. Let the path equation be
Initial height of the ball is,
Initial velocity,
Gravity,
Substitute the value into the model,
Thus, the model the path is
b.
To find: The time of flight of ball.
Given information:
The ball through upward at height 5 feet with vertical velocity of 50 feet per second.
Calculations:
The model the path is
When ball hit the ground from the maximum height.
Substitute
Time cannot be negative. So, the time of flight of ball is 3.222 seconds.
c.
To find: The maximum height of the ball.
Given information:
The ball through upward at height 5 feet with vertical velocity of 50 feet per second.
Calculations:
The model the path is
Three methods to find the maximum height:
- Vertex form
- Energy conservation
- Derivative method
First, method to find the maximum height. As it is parabolic path and the maximum at vertex.
The vertex of the path is
Thus, the maximum height is at 44.063 feet.
Energy conservation method: Total energy of the system is conserved.
Thus, the maximum height is 44.063 feet.
Find the maximum height using derivative method:
As the derivative is zero at maximum height.
For maximum height,
Substitute
Thus, the maximum height is 44.063.
Chapter 1 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education