### Physics Problem Explanation#### Problem 2: Soccer Ball Kick AnalysisGiven Scenario:- A soccer ball is kicked from ground level across a level soccer field.Parameters:1. **Initial Velocity (\( v_0 \))**: The ball has an initial velocity vector of \( 6 \, \text{m/s} \) at an angle of \( \theta = 34^\circ \) above the horizontal.2. **Vertical Motion**: The vertical motion remains unaffected by external factors.3. **Wind Resistance**: The ball experiences wind resistance causing a constant horizontal acceleration magnitude of \( q_h = -0.9 \, \text{m/s}^2 \).Objective:- Analyze the motion of the soccer ball using a Cartesian coordinate system.Instructions:- Assume any other air resistance is negligible.- Select a coordinate system with the origin at the ball's initial position.- Choose the positive direction of the reference frame from the initial point towards the final point of flight.Steps to Solve:1. Decompose the initial velocity into horizontal (\( v_{0x} \)) and vertical (\( v_{0y} \)) components: \[ v_{0x} = v_0 \cos(\theta) \] \[ v_{0y} = v_0 \sin(\theta) \]2. Account for wind resistance affecting horizontal motion: \[ a_x = q_h \]3. Analyze vertical motion unaffected by horizontal resistance: - Use kinematic equations for projectile motion.4. Employ a Cartesian coordinate system for detailed quantification of trajectories and impacts under given conditions.By understanding these parameters and assumptions, you can systematically approach the analysis of the problem, predict the trajectory of the soccer ball, and calculate the point of impact on the field. ### Problem Statement**Part (b)** Calculate the horizontal distance, \( x_{\text{max}} \), in meters, the ball travels before it returns to the soccer field.### Input Field\( x_{\text{max}} = \underline{\hspace{2cm}} \)### Calculation InterfaceA scientific calculator interface is provided with the following functions and buttons:#### Trigonometric and Hyperbolic Functions:- **sin()**- **cos()**- **tan()**- **cotan()**- **asin()** (inverse sine or arcsine)- **acos()** (inverse cosine or arccosine)- **atan()** (inverse tangent or arctangent)- **acotan()** (inverse cotangent or arccotangent)- **sinh()** (hyperbolic sine)- **cosh()** (hyperbolic cosine)- **tanh()** (hyperbolic tangent)- **cotanh()** (hyperbolic cotangent)#### Constants and Other Functions:- **π** (Pi)- **E** (Euler's Number)#### Selection for Angle Units:- **Degrees**- **Radians**#### Numbers and Operations:- Digits: **0** to **9**- **(** (left parenthesis)- **) ** (right parenthesis)- **.** (decimal point)- **+** (addition)- **-** (subtraction)- **/** (division)- **\*** (multiplication)- **√()** (square root)- **\^** (power)### Utility Buttons:- **Submit** (to submit the answer)- **Hint** (to get a hint for the problem)- **Feedback** (to view feedback)- **I give up!** (to give up and possibly view the correct answer or solution)### Submission Guidelines:- Attempts remain: Multiple (0% per attempt—deduction policy unmentioned).---Ensure to calculate \( x_{\text{max}} \) using the provided interface correctly and submit your answer. If needed, refer to hints and feedback options for guidance.

Initial velocity (v0) =6m/s Angle of projection (θ) =34° Horizontal deceleration (ax) = 0.98m/s2…

(10%) Problem 2: A soccer ball is kicked from ground level across a level soccer field with initial velocity vector vo= 6 m/s at soccer ball feels wind resistance 0=34° above horizontal. The which causes it to slow horizontally with constant acceleration magnitude a, = 0.98 m/s², while leaving its vertical motion unchanged. is negligible. Choose the positive direction of x from initial point towards final point of flight. Use a Cartesian system with the origin at the ball's initial position. Assume any other air resistance coordinate Williams Khalia-williams khalia@columbusstate.edu

(10%) Problem 2: A soccer ball is kicked from ground level across a level soccer field with initial velocity vector vo= 6 m/s at soccer ball feels wind resistance 0=34° above horizontal. The which causes it to slow horizontally with constant acceleration magnitude a, = 0.98 m/s², while leaving its vertical motion unchanged. is negligible. Choose the positive direction of x from initial point towards final point of flight. Use a Cartesian system with the origin at the ball's initial position. Assume any other air resistance coordinate Williams Khalia-williams khalia@columbusstate.edu

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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Concept explainers

Relative Velocity

It is a measurement of an object with regards to the other object which is moving or stable or stationary. For example, if we are traveling in a bus and the bus is moving at speed of 50km/hr, then our speed is according to the nearby passenger on the bus is zero. According to them, we are not moving. But if one person standing on the ground or road observes us from outside of the bus, according to him we are moving at a speed of 50km/hr and the bus is also moving at a speed of 50km/hr. Now, the motion is recognized by the observer, it depends on a frame of reference or observer. This is motion called relative motion.

Question

### Physics Problem Explanation

#### Problem 2: Soccer Ball Kick Analysis

Given Scenario:
- A soccer ball is kicked from ground level across a level soccer field.

Parameters:
1. **Initial Velocity (\( v_0 \))**: The ball has an initial velocity vector of \( 6 \, \text{m/s} \) at an angle of \( \theta = 34^\circ \) above the horizontal.
2. **Vertical Motion**: The vertical motion remains unaffected by external factors.
3. **Wind Resistance**: The ball experiences wind resistance causing a constant horizontal acceleration magnitude of \( q_h = -0.9 \, \text{m/s}^2 \).

Objective:
- Analyze the motion of the soccer ball using a Cartesian coordinate system.

Instructions:
- Assume any other air resistance is negligible.
- Select a coordinate system with the origin at the ball's initial position.
- Choose the positive direction of the reference frame from the initial point towards the final point of flight.

Steps to Solve:
1. Decompose the initial velocity into horizontal (\( v_{0x} \)) and vertical (\( v_{0y} \)) components:
\[
v_{0x} = v_0 \cos(\theta)
\]
\[
v_{0y} = v_0 \sin(\theta)
\]

2. Account for wind resistance affecting horizontal motion:
\[
a_x = q_h
\]

3. Analyze vertical motion unaffected by horizontal resistance:
- Use kinematic equations for projectile motion.

4. Employ a Cartesian coordinate system for detailed quantification of trajectories and impacts under given conditions.

By understanding these parameters and assumptions, you can systematically approach the analysis of the problem, predict the trajectory of the soccer ball, and calculate the point of impact on the field.

### Problem Statement
**Part (b)** Calculate the horizontal distance, \( x_{\text{max}} \), in meters, the ball travels before it returns to the soccer field.

### Input Field
\( x_{\text{max}} = \underline{\hspace{2cm}} \)

### Calculation Interface
A scientific calculator interface is provided with the following functions and buttons:

#### Trigonometric and Hyperbolic Functions:
- **sin()**
- **cos()**
- **tan()**
- **cotan()**
- **asin()** (inverse sine or arcsine)
- **acos()** (inverse cosine or arccosine)
- **atan()** (inverse tangent or arctangent)
- **acotan()** (inverse cotangent or arccotangent)
- **sinh()** (hyperbolic sine)
- **cosh()** (hyperbolic cosine)
- **tanh()** (hyperbolic tangent)
- **cotanh()** (hyperbolic cotangent)

#### Constants and Other Functions:
- **π** (Pi)
- **E** (Euler's Number)

#### Selection for Angle Units:
- **Degrees**
- **Radians**

#### Numbers and Operations:
- Digits: **0** to **9**
- **(** (left parenthesis)
- **) ** (right parenthesis)
- **.** (decimal point)
- **+** (addition)
- **-** (subtraction)
- **/** (division)
- **\*** (multiplication)
- **√()** (square root)
- **\^** (power)

### Utility Buttons:
- **Submit** (to submit the answer)
- **Hint** (to get a hint for the problem)
- **Feedback** (to view feedback)
- **I give up!** (to give up and possibly view the correct answer or solution)

### Submission Guidelines:
- Attempts remain: Multiple (0% per attempt—deduction policy unmentioned).

---

Ensure to calculate \( x_{\text{max}} \) using the provided interface correctly and submit your answer. If needed, refer to hints and feedback options for guidance.

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