3. Ezra is 4 feet tall. He threw a ball to Kira. The ball was released at an angle of 40° and he threw it with an initial speed of 22 feet per second. Assume the ball is thrown and caught at the top of the head of each child (their height). (Note: acceleration due to gravity is 32 ft/sec².) Write a vector function that describes the path of the ball.
3. Ezra is 4 feet tall. He threw a ball to Kira. The ball was released at an angle of 40° and he threw it with an initial speed of 22 feet per second. Assume the ball is thrown and caught at the top of the head of each child (their height). (Note: acceleration due to gravity is 32 ft/sec².) Write a vector function that describes the path of the ball.
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)...
Related questions
Question
Question is attached, thanks
![**Projectile Motion Problem: Vector Function for a Thrown Ball**
**Problem Statement:**
Ezra is 4 feet tall. He threw a ball to Kira. The ball was released at an angle of 40 degrees and he threw it with an initial speed of 22 feet per second. Assume the ball is thrown and caught at the top of the head of each child (their height).
(Note: acceleration due to gravity is \(32 \, \text{ft/sec}^2\).)
**Task:**
Write a vector function that describes the path of the ball.
**Explanation:**
To solve this problem, we need to model the motion of the ball using vector functions, considering both the horizontal and vertical components of the motion.
**Components of Motion:**
1. **Horizontal Motion:**
- Initial horizontal velocity, \(v_{x_0}\), is given by the formula:
\[
v_{x_0} = v_0 \cdot \cos(\theta)
\]
where
\(v_0 = 22 \, \text{ft/sec}\) and
\(\theta = 40^\circ\).
2. **Vertical Motion:**
- Initial vertical velocity, \(v_{y_0}\), is given by the formula:
\[
v_{y_0} = v_0 \cdot \sin(\theta)
\]
- The ball is subject to the acceleration due to gravity, \(g = 32 \, \text{ft/sec}^2\).
**Vector Function of the Path:**
The path of the ball can be expressed as a vector function \(\textbf{r}(t)\) where:
- The horizontal position as a function of time, \(x(t)\), is determined by:
\[
x(t) = v_{x_0} \cdot t
\]
- The vertical position as a function of time, \(y(t)\), is determined by:
\[
y(t) = y_0 + v_{y_0} \cdot t - \frac{1}{2}gt^2
\]
where \(y_0 = 4 \, \text{feet}\), the initial height of Ezra.
Putting it together, the vector function is:
\[
\textbf{r}(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F180a0b99-85bc-4289-89f8-874e199a7788%2Fa11da397-4327-4b20-b5c9-3e0a2657b34b%2F0jgl12g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Projectile Motion Problem: Vector Function for a Thrown Ball**
**Problem Statement:**
Ezra is 4 feet tall. He threw a ball to Kira. The ball was released at an angle of 40 degrees and he threw it with an initial speed of 22 feet per second. Assume the ball is thrown and caught at the top of the head of each child (their height).
(Note: acceleration due to gravity is \(32 \, \text{ft/sec}^2\).)
**Task:**
Write a vector function that describes the path of the ball.
**Explanation:**
To solve this problem, we need to model the motion of the ball using vector functions, considering both the horizontal and vertical components of the motion.
**Components of Motion:**
1. **Horizontal Motion:**
- Initial horizontal velocity, \(v_{x_0}\), is given by the formula:
\[
v_{x_0} = v_0 \cdot \cos(\theta)
\]
where
\(v_0 = 22 \, \text{ft/sec}\) and
\(\theta = 40^\circ\).
2. **Vertical Motion:**
- Initial vertical velocity, \(v_{y_0}\), is given by the formula:
\[
v_{y_0} = v_0 \cdot \sin(\theta)
\]
- The ball is subject to the acceleration due to gravity, \(g = 32 \, \text{ft/sec}^2\).
**Vector Function of the Path:**
The path of the ball can be expressed as a vector function \(\textbf{r}(t)\) where:
- The horizontal position as a function of time, \(x(t)\), is determined by:
\[
x(t) = v_{x_0} \cdot t
\]
- The vertical position as a function of time, \(y(t)\), is determined by:
\[
y(t) = y_0 + v_{y_0} \cdot t - \frac{1}{2}gt^2
\]
where \(y_0 = 4 \, \text{feet}\), the initial height of Ezra.
Putting it together, the vector function is:
\[
\textbf{r}(t) =
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
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…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON