Concept explainers
a.
Use a system of equations to find the equation of the parabola
a.
Answer to Problem 96E
Explanation of Solution
Given information:
A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. (
Calculation:
The given form of equation of parabola is,
Parabola passes through the points
Now parabola passes through the points
When parabola passes through the points
Now equation
Now use graphing calculator to write the matrix in reduced row-echelon form and we get the reduced row-echelon matrix,
Hence, the equation of parabola is,
b.
Use a graphing utility to graph the parabola.
b.
Answer to Problem 96E
Explanation of Solution
Given information:
A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. (
Calculation:
The graph of the parabola is as shown,
Hence, the graph of parabola is plotted.
c.
Graphically approximate the maximum height of the ball and the point at which the ball struck the ground.
c.
Answer to Problem 96E
Explanation of Solution
Given information:
A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. (
Calculation:
According to the graph the maximum height of the ball is
The point at which the ball struck the ground is
d.
Analytically find the maximum height of the ball and the point at which the ball struck the ground.
d.
Answer to Problem 96E
Explanation of Solution
Given information:
A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. (
Calculation:
Consider the equation of parabola
Now calculate the maximum height of the ball with calculus theory,
For a function
Now we have,
Now the maximum height is put
Now the point at which the ball struck the ground is,
Hence, calculated results are
e.
Compare your results from parts (c) and (d).
e.
Answer to Problem 96E
Both results are similar.
Explanation of Solution
Given information:
A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. (
Calculation:
The result from graphically and analytically method, both are similar.
Hence, both results are similar.
Chapter 8 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning