Concept explainers
To calculate the time for which the rocket was in the air.
Answer to Problem 9CYU
The time for which the rocket was in the air is 8.4 seconds.
Explanation of Solution
Given information :
The function provided is
Formula used :
To find the time that the rocket was in the air, calculate the x-intercept. This can be done by graphing the given equation and checking the root of the same.
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.
Calculation :
The graph of the given equation is
In this, the parabola one x-intercept at the origin, that is (0,0). 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 closest to 0 will be the roots of the equation.
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 | 43.74 | 31.16 | 18.26 | 5.04 | -8.5 | -22.36 | -36.54 | -51.04 | -65.86 |
In the table, the value of y that is closest to 0 is 5.04. Their corresponding x value would be the root.
Thus, 0 and 8.4 are the roots. Hence the rocket reaches the ground after 8.4 seconds.
Chapter 9 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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