a.
To Find: the equation of parabola that passes through the points.
a.
Answer to Problem 94E
The equation of parabola is
Explanation of Solution
Given information:
A video of the path of 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 timethe coordinates obtained are shown in the table (x and y are measured in feet)
Calculation:
Given the equation of parabola:
Putting
Putting
Putting
Equation 1:
Equation 2:
Equation 3:
Now solving this system of equation
Augmented matrix:
Reducing this augmented matrix in echelon form
Now system of linear equation according to echelon matrix
Hence the equation of parabola is
b.
To Graph: use a graphing utility to graph the parabola
b.
Explanation of Solution
Given information:
Graph:
c.
To Find: maximum height of the ball and the point at which the ball strikes the ground.
c.
Answer to Problem 94E
Maximum height of the ball is:
The point at which the ball strikes the ground:
Explanation of Solution
Graph:
Interpretation:
From graph it is clear that
Maximum height of the ball is:
The point at which the ball strikes the ground:
d.
To Find: Algebraically, the maximum height of the ball and the point at which the ball strikes the ground
d.
Answer to Problem 94E
The maximum height of the ball is
The point at which the ball strikes the ground is
Explanation of Solution
Given:
Calculation:
The equation of parabola is
Maximum height of parabola occurs at its vertex so converting the equation into standard form that is
Where
Therefore, Maximum height of parabola is
Therefore putting
Reject
Therefore, the ball strikes the ground at
Chapter 7 Solutions
Precalculus with Limits: A Graphing Approach
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