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Need help with Investigation 2.2. On plotting the range vs. the angle, and to determine the angle of maximum range.

Need help with Investigation 2.2. On plotting the range vs. the angle, and to determine the angle of maximum range.

College Physics
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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Need help with Investigation 2.2. On plotting the range vs. the angle, and to determine the angle of maximum range. Thanks! 

## Lab 5: Two-Dimensional Motion ### Objectives: - To study two-dimensional motion - To understand the vector nature of velocity - To understand the independence of motion in the x- and y- directions ### Equipment: - Ballistic gun - Plain paper - Carbon paper - Meter stick --- ### Introduction: In this lab, you will be firing a ball from a ballistic gun. The set-up is shown in the picture below. You can vary the initial angle and measure the initial height and the distance the ball travels in the x direction. You will be making measurements in order to determine the initial velocity of the ball. You will also examine the dependence of the distance traveled in the x-direction on the initial angle. --- ### Explanation of Diagram: **Figure 1: Projectile Motion** The diagram illustrates the setup and measurement parameters for the experiment. - **Ballistic Gun**: The device used to launch the ball. - **Trigger**: Mechanism to release the ball from the ballistic gun. - **Plumb**: Tool used to ensure measurements of angles and heights are accurate and vertical. - **Table Top**: The flat surface from which the ball is launched. - **Trajectory Path**: The curved path that the ball follows after being fired from the ballistic gun. - **H**: Represents the initial height from the table top to the ground. - **X and y components**: Directions along which the ball moves, where x is horizontal and y is vertical. - **R**: The range or horizontal distance traveled by the ball. - **Vx**: The horizontal component of the ball's velocity. This setup allows for the precise study of two-dimensional motion by isolating and examining the variables involved, such as initial velocity, trajectory angle, and distances traveled. --- These explanations and the diagram will help you understand the principles of two-dimensional motion and how to measure and analyze them in this lab exercise.
Transcribed Image Text:## Lab 5: Two-Dimensional Motion ### Objectives: - To study two-dimensional motion - To understand the vector nature of velocity - To understand the independence of motion in the x- and y- directions ### Equipment: - Ballistic gun - Plain paper - Carbon paper - Meter stick --- ### Introduction: In this lab, you will be firing a ball from a ballistic gun. The set-up is shown in the picture below. You can vary the initial angle and measure the initial height and the distance the ball travels in the x direction. You will be making measurements in order to determine the initial velocity of the ball. You will also examine the dependence of the distance traveled in the x-direction on the initial angle. --- ### Explanation of Diagram: **Figure 1: Projectile Motion** The diagram illustrates the setup and measurement parameters for the experiment. - **Ballistic Gun**: The device used to launch the ball. - **Trigger**: Mechanism to release the ball from the ballistic gun. - **Plumb**: Tool used to ensure measurements of angles and heights are accurate and vertical. - **Table Top**: The flat surface from which the ball is launched. - **Trajectory Path**: The curved path that the ball follows after being fired from the ballistic gun. - **H**: Represents the initial height from the table top to the ground. - **X and y components**: Directions along which the ball moves, where x is horizontal and y is vertical. - **R**: The range or horizontal distance traveled by the ball. - **Vx**: The horizontal component of the ball's velocity. This setup allows for the precise study of two-dimensional motion by isolating and examining the variables involved, such as initial velocity, trajectory angle, and distances traveled. --- These explanations and the diagram will help you understand the principles of two-dimensional motion and how to measure and analyze them in this lab exercise.
### Investigation 2: Range **Objective:** Explore the dependence of the range on the angle for the case where the ball starts and ends at the same height (y = y₀ = 0). --- **Investigation 2.1:** Fire the ball from the table at 10 different angles, from 30° to 75°. Measure the range (distance travelled in the x-direction) for each of those angles. (Make three measurements for each angle and take the average range.) Record your data in the table below. | **Angle (°)** | **Range 1st Measurement (cm)** | **Range 2nd Measurement (cm)** | **Range 3rd Measurement (cm)** | **Average Range (cm)** | |---------------|--------------------------------|--------------------------------|--------------------------------|------------------------| | 30° | 81.2 cm | 80.3 cm | 81.4 cm | 80.9 cm | | 35° | 85.5 cm | 84.5 cm | 85.1 cm | 85.0 cm | | 40° | 88.2 cm | 90.5 cm | 90.6 cm | 89.8 cm | | 45° | 91.3 cm | 91.7 cm | 92.7 cm | 91.9 cm | | 50° | 88.8 cm | 90.3 cm | 90.0 cm | 89.7 cm | | 55° | 85.7 cm | 85.3 cm | 86.2 cm | 85.7 cm | | 60° | 76.9 cm | 77.0 cm | 77.5 cm | 77.1 cm | | 65° | 70.0 cm | 69.8 cm | 70.3 cm | 70.0 cm | | 70° | 68.9 cm | 70.1 cm | 70.3 cm | 69.8 cm | | 75° | 50.0 cm | 52.2 cm | 52.4 cm |
Transcribed Image Text:### Investigation 2: Range **Objective:** Explore the dependence of the range on the angle for the case where the ball starts and ends at the same height (y = y₀ = 0). --- **Investigation 2.1:** Fire the ball from the table at 10 different angles, from 30° to 75°. Measure the range (distance travelled in the x-direction) for each of those angles. (Make three measurements for each angle and take the average range.) Record your data in the table below. | **Angle (°)** | **Range 1st Measurement (cm)** | **Range 2nd Measurement (cm)** | **Range 3rd Measurement (cm)** | **Average Range (cm)** | |---------------|--------------------------------|--------------------------------|--------------------------------|------------------------| | 30° | 81.2 cm | 80.3 cm | 81.4 cm | 80.9 cm | | 35° | 85.5 cm | 84.5 cm | 85.1 cm | 85.0 cm | | 40° | 88.2 cm | 90.5 cm | 90.6 cm | 89.8 cm | | 45° | 91.3 cm | 91.7 cm | 92.7 cm | 91.9 cm | | 50° | 88.8 cm | 90.3 cm | 90.0 cm | 89.7 cm | | 55° | 85.7 cm | 85.3 cm | 86.2 cm | 85.7 cm | | 60° | 76.9 cm | 77.0 cm | 77.5 cm | 77.1 cm | | 65° | 70.0 cm | 69.8 cm | 70.3 cm | 70.0 cm | | 70° | 68.9 cm | 70.1 cm | 70.3 cm | 69.8 cm | | 75° | 50.0 cm | 52.2 cm | 52.4 cm |
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