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Exploration 2.1 Consider the case where the ball lands at the same level tħat it is fired. The range of the ball (distance travelled in the x- direction) can be determined in terms of the initial velocity, v, the initial angle, 0, and the gravitational constant, g. Use the equations of motion in both the x- and y- directions to determine the equation for the range. (Don't just write the equation down. Show your work on how it is derived.)

Exploration 2.1 Consider the case where the ball lands at the same level tħat it is fired. The range of the ball (distance travelled in the x- direction) can be determined in terms of the initial velocity, v, the initial angle, 0, and the gravitational constant, g. Use the equations of motion in both the x- and y- directions to determine the equation for the range. (Don't just write the equation down. Show your work on how it is derived.)

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 answering exploration 1.2 and exploration 2.2 thanks!

### Exploration 2: Angular Dependence of Range on Angle **Exploration 2.1:** Consider the case where the ball lands at the same level that it is fired. The range of the ball (distance travelled in the x-direction) can be determined in terms of the initial velocity, \( v_0 \), the initial angle \( \theta \), and the gravitational constant, \( g \). Use the equations of motion in both the x- and y-directions to determine the equation for the range. Show your work on how it is derived. (Don’t just write the equation down.)
Transcribed Image Text:### Exploration 2: Angular Dependence of Range on Angle **Exploration 2.1:** Consider the case where the ball lands at the same level that it is fired. The range of the ball (distance travelled in the x-direction) can be determined in terms of the initial velocity, \( v_0 \), the initial angle \( \theta \), and the gravitational constant, \( g \). Use the equations of motion in both the x- and y-directions to determine the equation for the range. Show your work on how it is derived. (Don’t just write the equation down.)
### Physics Exploration Activities #### Exploration 1.2: Initial and Final Positions Measurement You will be measuring the initial and final positions, but not the time of travel. The time of travel is the same in both the x and y directions. Solve the kinematics equations for the initial velocity of the ball in terms of fundamental constants and quantities you can measure, such as initial and final positions. Show your work and write the equations in the space below. #### Exploration 1.3: Firing the Ball at Different Angles If you fire the ball at a different angle (≠ 0), will the initial velocity be the same or different from the horizontal case? Explain the difference in the two cases. **Student Handwritten Response:** It will be different because when fired horizontally, only the horizontal component of velocity is there. At an angle, the initial velocity is split into horizontal and vertical components. --- #### Explanation of Diagrams (If Applicable) There appears to be a faint and partially visible diagram on the page which might be illustrating the trajectory of a projectile or the setup for the kinematics experiment. However, due to the faintness and incomplete visibility, it is challenging to provide a full description of the diagram. This activity is designed to enhance your understanding of the kinematic equations and the impact of different forces and angles on the motion of a projectile. Make sure to analyze and measure carefully to determine the initial velocities accurately. Your observations and detailed equations will provide deeper insights into the fundamentals of projectile motion.
Transcribed Image Text:### Physics Exploration Activities #### Exploration 1.2: Initial and Final Positions Measurement You will be measuring the initial and final positions, but not the time of travel. The time of travel is the same in both the x and y directions. Solve the kinematics equations for the initial velocity of the ball in terms of fundamental constants and quantities you can measure, such as initial and final positions. Show your work and write the equations in the space below. #### Exploration 1.3: Firing the Ball at Different Angles If you fire the ball at a different angle (≠ 0), will the initial velocity be the same or different from the horizontal case? Explain the difference in the two cases. **Student Handwritten Response:** It will be different because when fired horizontally, only the horizontal component of velocity is there. At an angle, the initial velocity is split into horizontal and vertical components. --- #### Explanation of Diagrams (If Applicable) There appears to be a faint and partially visible diagram on the page which might be illustrating the trajectory of a projectile or the setup for the kinematics experiment. However, due to the faintness and incomplete visibility, it is challenging to provide a full description of the diagram. This activity is designed to enhance your understanding of the kinematic equations and the impact of different forces and angles on the motion of a projectile. Make sure to analyze and measure carefully to determine the initial velocities accurately. Your observations and detailed equations will provide deeper insights into the fundamentals of projectile motion.
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