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 \( V_o \).

Answered: Image /qna-images/answer/fcc9e6ea-6438-4490-88ce-20f7b75de86d.jpg

Now assuming negligible aerodynamic drag, the equations governing the "flight" of the ball are given as: x = xo +Voxt 1 29t² y = yo + Voyt - 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 = ax² + bx + c Perform this process and compare the result to the trendline equation to determine the "launch" speed of the ball Vo.

Now assuming negligible aerodynamic drag, the equations governing the "flight" of the ball are given as: x = xo +Voxt 1 29t² y = yo + Voyt - 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 = ax² + bx + c Perform this process and compare the result to the trendline equation to determine the "launch" speed of the ball Vo.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Static and Kinetic Friction

Kinetic friction comes into existence when there are moving surfaces means in other words we can say that the force which comes into existing between moving surfaces is known as kinetic friction.

Question

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 \( V_o \).

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