**Educational Website Content**---**Title: Calculating Kinetic Energy and Potential Energy Equivalence in Baseball****Introduction:**Professional baseball pitchers deliver pitches that can reach the blazing speed of 100 mph (miles per hour). A local team has drafted an up-and-coming, left-handed pitcher who can consistently pitch at 42.68 m/s (95.50 mph). Let's explore the physics behind this scenario by calculating the kinetic energy of the baseball and the equivalent height it must be dropped from to have the same energy due to gravity.**Problem Statement:**Assuming a pitched ball has a mass of 0.1420 kg and has this speed just before a batter makes contact with it, how much kinetic energy does the ball have?\[ K_{\text{ball}} = \] ________ J**Further Analysis:**Recall that the acceleration due to gravity is \( 9.81 \, \text{m/s}^2 \). How high would the ball need to be dropped from to attain the same energy as it did when it was pitched (neglect air resistance)?\[ h_{\text{ball}} = \] ________ m**Discussion:*** In the first part of this exercise, students will calculate the kinetic energy using the formula: \[ K_{\text{ball}} = \frac{1}{2} m v^2 \] where \( m \) is the mass of the ball (0.1420 kg) and \( v \) is the velocity (42.68 m/s). * In the second part, students will use the potential energy formula to find the height: \[ PE = mgh \] where \( PE \) is the potential energy equivalent to the kinetic energy, \( g \) is the acceleration due to gravity, and \( h \) is the height.**Conclusion:**This exercise helps in understanding the transformation of kinetic energy to potential energy and vice versa, demonstrating core principles of physics in everyday sports scenarios. ---

Answered: Image /qna-images/answer/c5a5b141-4880-42db-a58c-dad19181fdcb.jpg

a mass of 0.1420 kg and has this speed just before a batter makes contact with it, how much kinetic energy does the ball have? Kpall = J Recall that the acceleration due to gravity is 9.81m/s2. How high would the ball need to be dropped from to attain the same energy as it did when it was pitched (neglect air resistance)?

a mass of 0.1420 kg and has this speed just before a batter makes contact with it, how much kinetic energy does the ball have? Kpall = J Recall that the acceleration due to gravity is 9.81m/s2. How high would the ball need to be dropped from to attain the same energy as it did when it was pitched (neglect air resistance)?

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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