**Conservation of Energy, Projectile Motion, Acceleration x, y, z**A marble of weight = 5 lb is launched thanks to a spring on a ramp.The spring has a coefficient of rigidity of k = 5 lb/ft, an unstretched length of s0 = 7 ft.The ramp is l = 9 ft long and h = 5 ft tall.![diagram]In the diagram:- A spring (denoted by the symbol K) is compressed and launches the marble up a ramp.- The ramp is inclined and leads to point A, where the marble has a velocity \( v_A \).- The point A is the beginning of the projectile motion path.- The path from point A to point C shows the projectile trajectory of the marble with a parabolic shape.- Point B represents the maximum altitude \( h_{\text{max}} \) of the marble’s flight.- The horizontal distance from point A to point C is labeled as the Range.**Given:**If the velocity at A is \( v_A = 9 \) ft/s, find:1. The displacement of the spring needed to reach this velocity.2. The range of the flight.3. The maximum altitude of the flight.**Instructions for solving the problems:**1. **Displacement of the Spring:** - Use energy conservation principles to connect the spring displacement to the launch velocity \( v_A \).2. **Range of the Flight:** - Use projectile motion equations to find the range. This involves decomposing the launch velocity into horizontal and vertical components.3. **Maximum Altitude of the Flight:** - Use kinematic equations to find the maximum altitude.**Example Equations:**1. Spring Potential Energy: \( \frac{1}{2} k x^2 \)2. Kinematic Equations for Projectile Motion.3. Energy Conservation: Potential Energy of the Spring = Kinetic Energy at A.**Input Instructions:**In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question 3).---**Note on the Diagram:**- The inclined plane (ramp) is marked with its length and height.- The spring is shown compressed at the bottom of the ramp.- The trajectory from A to C is a dashed curve, indicating the parabolic path of the projectile.- Arrows and labels indicate key quantities to be calculated

Conservation of Energy, Projectile Motion, Acceleration x, y, z. A marble of weight=5lb is launch thanks to a spring on a ramp. The spring has a coefficient of rigidity of = 5lb/ft, an unstretched length of s0=7ft. The ramp is 1=9ft long and h=5ft tall. k www. е VA h Th max Range If the velocity at A is vA=9ft/s find: 1. The displacement of the spring needed to reach this velocity. 2. The range of the flight. 3. The maximum altitude of the flight. с In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question3).

Conservation of Energy, Projectile Motion, Acceleration x, y, z. A marble of weight=5lb is launch thanks to a spring on a ramp. The spring has a coefficient of rigidity of = 5lb/ft, an unstretched length of s0=7ft. The ramp is 1=9ft long and h=5ft tall. k www. е VA h Th max Range If the velocity at A is vA=9ft/s find: 1. The displacement of the spring needed to reach this velocity. 2. The range of the flight. 3. The maximum altitude of the flight. с In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question3).

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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