Can someone help me by answering all questions. **Projectile Motion Exploration****Part 1: Warm-up** Determine the angle that maximizes the range of a projectile when fired across a flat surface.*Diagram Description:* The diagram illustrates a projectile path with an arrow indicating the angle \( \theta \) and defining the "Range" as the horizontal distance traveled by the projectile.**Tasks:**1. **Maximum Range Calculation:** - Calculate the maximum range if the projectile speed is 3.0 m/s.2. **Specific Angle Calculation:** - Find the range of the projectile if it is fired at 20 degrees above the horizon. Provide a numerical value for your answer.3. **General Angle Calculation:** - Derive an algebraic expression for the range when the projectile is fired at an arbitrary angle \( \theta \).4. **Range Equation Analysis:** - Solve for the angle \( \theta \) when the range \( R = 0 \). - Provide an explanation of why certain angles result in zero range. - Illustrate the projectile's trajectory for angles that yield zero range.5. **Graphical Representation:** - Sketch a graph showing the relationship between range and angle \( \theta \).6. **Optimal Angle Investigation:** - Determine the angle \( \theta \) for which the range is maximized. - Use calculus by differentiating the range equation \( \frac{dR}{d\theta} \), setting the derivative equal to zero, and solving for \( \theta \).7. **Table Launch Scenario:** - Calculate the range when the projectile is fired at 20 degrees above the horizon and launched from a table 2.0 meters high.8. **Experimental Comparison:** - Repeat previous steps for an arbitrary angle \( \theta \) and height \( h \). - Compare theoretical results with experimental data collected in a lab.This educational module aims to deepen understanding of projectile motion dynamics and their practical applications through theoretical analysis and experimental validation.

NOTE : As per bartleby guidelines , we can answer only first three sub-parts [part 1, a, b]of a…

Part 1) Warm-up: What is the angle that maximizes the range of a projectile if fired across a flat surface (see below) Range Find the max range if the projectile speed is 3.0 m/s. a) Find the range of the projectile if it is fired at 20. degrees above the horizon. Write your answer as a numerical value. b) Find the range of the projectile if it is fired at an arbitrary angle ". Write your answer as an algebraic expression.

Part 1) Warm-up: What is the angle that maximizes the range of a projectile if fired across a flat surface (see below) Range Find the max range if the projectile speed is 3.0 m/s. a) Find the range of the projectile if it is fired at 20. degrees above the horizon. Write your answer as a numerical value. b) Find the range of the projectile if it is fired at an arbitrary angle ". Write your answer as an algebraic expression.

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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