
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Transcribed Image Text:In each my sections of MCEG 1101 (P01 & P02), a student was asked to toss a tennis ball in front of the screen upon which a grid was projected. Based on my slow-motion video recording of the ball tossed in Section P01, the following data was generated (also see uploaded Excel file "tennis ball toss trajectory").
| x (grid units) | y (grid units) | x(ft) | y(ft) |
|----------------|----------------|-------|-------|
| 1 | 0 | 0.55 | 0 |
| 2 | 3 | 1.1 | 1.65 |
| 3 | 5.3 | 1.65 | 2.915 |
| 4 | 6.5 | 2.2 | 3.575 |
| 5 | 6.7 | 2.75 | 3.685 |
| 6 | 5.8 | 3.3 | 3.19 |
| 7 | 4 | 3.85 | 2.2 |
| 8 | 0.9 | 4.4 | 0.495 |
Based on these data, a parabolic trendline was developed, as shown in the plot below:
**Tennis Ball Toss Data from MCEG 1101-P01:**
A graph is depicted with the following details:
- **Title:** Tennis Ball Toss Data from MCEG 1101-P01
- **Axes Labels:**
- Horizontal axis (x-axis): horizontal position, x (ft), ranging from 0 to 5.
- Vertical axis (y-axis): vertical position, y (ft), ranging from 0 to 4.
- **Data Points:** Plot shows blue circular markers indicating the data points plotted along with a light blue dotted trendline illustrating the parabolic trajectory of the tennis ball.
- **Equation of the Parabola:** The equation of the trendline is \( y = -0.9307x^2 + 4.7619x - 2.3925 \).
- **Coefficient of Determination:** \( R^2 = 0.999 \), suggesting a very good fit to the data.
![Now, assuming negligible aerodynamic drag, the equations governing the "flight" of the ball are given as:
\[ x = x_o + V_{ox}t \]
\[ y = y_o + V_{oy}t - \frac{1}{2}gt^2 \]
The first of these equations can be used to isolate \( t \) and express it as a function of \( x \) (as done in class). Then this expression for \( t \) can be substituted into the second equation to obtain an equation for \( y \) as a function of \( x \) (as done in class). Finally, this equation can be simplified and put into the standard form of:
\[ y = ax^2 + bx + c \]
Perform this process and compare the result to the trendline equation to determine the "launch" speed of the ball \( V_o \).](https://content.bartleby.com/qna-images/question/b6a5dc36-f8ad-4b33-b7c1-442868d13e4d/fcc9e6ea-6438-4490-88ce-20f7b75de86d/d3e8s97_thumbnail.jpeg)
Transcribed Image Text:Now, assuming negligible aerodynamic drag, the equations governing the "flight" of the ball are given as:
\[ x = x_o + V_{ox}t \]
\[ y = y_o + V_{oy}t - \frac{1}{2}gt^2 \]
The first of these equations can be used to isolate \( t \) and express it as a function of \( x \) (as done in class). Then this expression for \( t \) can be substituted into the second equation to obtain an equation for \( y \) as a function of \( x \) (as done in class). Finally, this equation can be simplified and put into the standard form of:
\[ y = ax^2 + bx + c \]
Perform this process and compare the result to the trendline equation to determine the "launch" speed of the ball \( V_o \).
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