Concept explainers
A Falling Ball In a physics experiment a lead ball is dropped from a height of 5 m. The students record the distance the ball has fallen every one-tenth of a second. (This can be done by using a camera and a strobe light.) Their data are shown in the margin.
- (a) Make a
scatter plot of the data. - (b) Use a calculator to find a power model.
- (c) Use your model to predict how far a dropped ball would fall in 3 s.
Time (s) | Distance (m) |
0.1 | 0.048 |
0.2 | 0.197 |
0.3 | 0.441 |
0.4 | 0.882 |
0.5 | 1.227 |
0.6 | 1.765 |
0.7 | 2.401 |
0.8 | 3.136 |
0.9 | 3.969 |
1.0 | 4.902 |
(a)
To sketch: The scatter plot of the data.
Explanation of Solution
Given:
In a physics experiment a lead ball is drops from a height of 5 m, the students’ record the distance the ball has fallen every one-tenth of a second listed below in Table 1.
0.1 | 0.048 |
0.2 | 0.197 |
0.3 | 0.441 |
0.4 | 0.882 |
0.5 | 1.227 |
0.6 | 1.765 |
0.7 | 2.401 |
0.8 | 3.136 |
0.9 | 3.969 |
1.0 | 4.902 |
Table 1
Calculation:
Use online graphing calculator and draw the scatter plot of the given data as shown below in Figure 1.
Form Figure 1, it is noticed that the scatter plot is an increasing function.
(b)
To find: The power model for the given data by using calculator.
Answer to Problem 2P
The power model that best fits the data point for the given data is
Explanation of Solution
Let
Use online graphing calculator and obtain the power regression line as follows.
Input time data as x values and
From above screenshot, it is noticed that the power model that best fits the data point is
Therefore, the power model that best fits the data point for the given data is
(c)
To predict: The distance for a dropped ball would fall in 3 seconds.
Answer to Problem 2P
The fallen distance of the dropped ball in 3 seconds
Explanation of Solution
From part (b) the power model that best fits the data point for the given data is
Substitute
Therefore, the fallen distance of the dropped ball in 3 seconds is
Chapter 4 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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