College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

bartleby

Concept explainers

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.
expand button
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 \( V_o \).
expand button
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 \( V_o \).
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON