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)...
icon
Related questions
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.
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 \( V_o \).
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
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Nonconservative forces
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
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON