### Problem StatementA boy whirls a stone in a horizontal circle of radius 1.83 m and at a height of 2.38 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 9.15 m. What is the magnitude of the centripetal acceleration of the stone while in circular motion? Use \( g = 9.81 \, \text{m/s}^2 \).### Input Fields- **Number**: [Enter your solution here]- **Units**: [Select appropriate units from a dropdown list] ### ExplanationThis problem involves calculating the magnitude of the centripetal acceleration of an object in horizontal circular motion before it is released and projected horizontally.### Key Concepts- **Centripetal Acceleration (\(a_c\))**: The acceleration directed towards the center of a circle that keeps an object moving in a circular path.- **Projectile Motion**: Once the stone is released, it follows a projectile motion path under the influence of gravity only. ### Steps to Solve1. **Determine the Time of Flight**: - Calculate how long it takes for the stone to fall 2.38 m vertically using the kinematic equation for vertical motion under gravity. 2. **Calculate the Initial Horizontal Velocity**: - Use the horizontal distance traveled (9.15 m) and the time of flight to find the initial horizontal velocity, which is the same as the velocity of the stone in the circular motion before release. 3. **Calculate the Centripetal Acceleration**: - Use the formula for centripetal acceleration: \[ a_c = \frac{v^2}{r} \] Where \( v \) is the velocity and \( r \) is the radius of the circle.### Notes- Ensure all the units are consistent.- Use given gravitational acceleration \( g = 9.81 \, \text{m/s}^2 \) for calculations.By following these steps and understanding these principles, the solution to the problem can be systematically derived.

A boy whirls a stone in a horizontal circle of radius 1.83 m and at height 2.38 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 9.15 m. What is the magnitude of the centripetal acceleration of the stone while in circular motion? Use g=9.81 m/s². Number i Units

A boy whirls a stone in a horizontal circle of radius 1.83 m and at height 2.38 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 9.15 m. What is the magnitude of the centripetal acceleration of the stone while in circular motion? Use g=9.81 m/s². Number i Units

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter6: Applications Of Newton’s Laws Of Motion

Section: Chapter Questions

Problem 51PQ: Harry Potter decides to take Pottery 101 as an elective to satisfy his arts requirement at Hog...

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