### Example Problem: Speed vs. Height of a Tossed BallThe figure below shows the speed \( v \) versus height \( y \) of a ball tossed directly upward along a y-axis. - Distance \( d \) is 0.40 m.- The speed at height \( y_A \) is \( v_A \).- The speed at height \( y_B \) is \( \frac{1}{3} v_A \).**Question:** What is speed \( v_A \) in terms of the given quantities?**Given:** Use \( g = 10 \, \text{m/s}^2 \).#### Diagram Explanation:The graph displays the relationship between speed (\( v \)) and height (\( y \)) for the ball. Key points to note from the graph:1. The vertical axis (y-axis) represents speed \( v \).2. The horizontal axis (x-axis) represents height \( y \).3. There are horizontal dashed lines indicating speeds \( v_A \) and \( \frac{1}{3} v_A \).4. Heights \( y_A \) and \( y_B \) are marked on the \( y \)-axis with \( d \) as the distance between \( y_A \) and \( y_B \).The graph suggests a downward-opening parabolic relationship between \( v \) and \( y \).The goal is to determine the speed \( v_A \) using the provided information and the given acceleration due to gravity \( g \).#### Detailed Solution:To solve for \( v_A \), we analyze the energy changes when the ball moves from height \( y_A \) to \( y_B \).1. **Kinetic Energy at \( y_A \):** \[ K.E. = \frac{1}{2} m v_A^2 \]2. **Kinetic Energy at \( y_B \):** \[ K.E. = \frac{1}{2} m \left( \frac{1}{3} v_A \right)^2 = \frac{1}{2} m \left( \frac{1}{9} v_A^2 \right) = \frac{1}{18} m v_A^2 \]3. **Potential Energy Change:** \[ \Delta P.E. = m g d = m \times

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The Figure below shows the speed v versus height y of a ball tossed directly upward, along a y-axis. Distance d is 0.40 m. The speed at height ya is vA. The speed at height yg is VA. VWhat is VA speed va in terms of the given quantities? (Use g 10 m/s?.)

The Figure below shows the speed v versus height y of a ball tossed directly upward, along a y-axis. Distance d is 0.40 m. The speed at height ya is vA. The speed at height yg is VA. VWhat is VA speed va in terms of the given quantities? (Use g 10 m/s?.)

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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