Concept explainers
To calculate the number of seconds taken by the ball to reach the ground.
Answer to Problem 21MCQ
The time taken by the ball to reach the ground is 8.1 seconds.
Explanation of Solution
Given information :
The function provided is
Formula used :
The given equation would be graphed as a function and the points of x-intercepts would be the results. For these points, the x-coordinate shall serve the purpose of the results.
Since the roots are not on points that are integers, use the approximation method to compute the roots.
The roots would be the time taken by the ball to reach the ground. If the root is negative, discard the root as it is assumed that the ball will be launched from a height of 25 feet at
Calculation :
The graph of the given equation is
In this, the parabola one x-intercept is between -4 and -3. The other x-intercept is between 8 and 9.
To find the roots, make a table of values for x in between these points with intervals on 0.1 . The value of x that is result closest to 0 will be the roots of the equation.
Since the time cannot be negative, discard the root between -4 and -3.
Table of values in between 8 and 9
x | 8.1 | 8.2 | 8.3 | 8.4 | 8.5 | 8.6 | 8.7 | 8.8 | 8.9 |
y | -0.11 | -1.24 | -2.39 | -3.56 | -4.75 | -5.96 | -7.19 | -8.44 | -9.71 |
In the tables, the value of y that is closest to 0 is -0.11. Their corresponding x values would be the roots.
Thus, 8.1 is the root.
Hence, time taken by the ball to reach the ball is 8.1 seconds.
Chapter 9 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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