**Physics Problem Explanation: Trampoline Kinetic Energy****Problem Statement:**A 28-kg girl is bouncing on a trampoline. During a certain interval after leaving the surface of the trampoline, her kinetic energy decreases to 220 J from 420 J. How high does she rise during this interval? Neglect air resistance.**Solution:**To solve this problem, we can use the principle of conservation of energy. The loss in kinetic energy will equal the gain in potential energy as she rises.1. Initial kinetic energy (\(KE_i\)) = 420 J2. Final kinetic energy (\(KE_f\)) = 220 J**Step 1: Calculate the change in kinetic energy:**\[\Delta KE = KE_i - KE_f\]\[\Delta KE = 420 \text{ J} - 220 \text{ J} = 200 \text{ J}\]**Step 2: Relate this change to potential energy:**The change in kinetic energy will be equal to the change in potential energy since air resistance is neglected:\[\Delta KE = \Delta PE\]**Step 3: Use the potential energy formula:**Potential energy (\(PE\)) gained by the girl as she rises:\[PE = mgh\]Where:- \(m\) is the mass (28 kg)- \(g\) is the acceleration due to gravity (9.8 m/s²)- \(h\) is the height she rises**Step 4: Solve for height (\(h\)):**\[200 \text{ J} = (28 \text{ kg})(9.8 \text{ m/s}^2)(h)\]\[200 \text{ J} = 274.4 \text{ kg} \cdot \text{m/s}^2 \cdot h\]\[h = \frac{200 \text{ J}}{274.4 \text{ kg} \cdot \text{m/s}^2}\]\[h \approx 0.73 \text{ m}\]**Conclusion:**The girl rises approximately 0.73 meters during this interval when her kinetic energy decreases from 420 J to 220 J.

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A 28-kg girl is bouncing on a trampoline. During a certain interval after leaving the surface of the trampoline, her kinetic energy decreases to 220 J from 420 J. How high does she rise during this interval? Neglect air resistance.

A 28-kg girl is bouncing on a trampoline. During a certain interval after leaving the surface of the trampoline, her kinetic energy decreases to 220 J from 420 J. How high does she rise during this interval? Neglect air resistance.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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