### Roller Coaster Dynamics#### Diagram Explanation:The image depicts a roller coaster track with a loop and a descent. Key points are marked as follows:- **Point A**: The starting point at the top left, where the roller coaster begins its motion.- **Point B**: Positioned at the midpoint of the loop. It is highlighted with a vertical measurement of 7.5 meters.- **Point C**: A flat section following the loop.- **Height (h)**: The maximum vertical height from the ground to Point A, which needs determining.- The total vertical distance from the base to the maximum height of the track is denoted as 20 meters.#### Problem Statement:The roller coaster car has a mass of 159 kg and a speed of 3 m/s at Point A. The task is to determine the minimal height (h) for the starting point A if the track is designed so that the car does not leave the track at Point B.This is a classic problem in physics, involving concepts of energy conservation and dynamics, where the potential and kinetic energy at different points on the track determine the minimum height required at the starting point.

Answered: Image /qna-images/answer/2171feea-9c43-41aa-bd07-ce61a49d977e.jpg

Answered: A B 7.5 m h 20 m The roller coaster car…

A B 7.5 m h 20 m The roller coaster car having a mass of 159-kg has a speed of 3 m/s at A. Determine the minimal height h of A if the track is designed so that the car does not leave it at B.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Question

### Roller Coaster Dynamics

#### Diagram Explanation:

The image depicts a roller coaster track with a loop and a descent. Key points are marked as follows:

- **Point A**: The starting point at the top left, where the roller coaster begins its motion.
- **Point B**: Positioned at the midpoint of the loop. It is highlighted with a vertical measurement of 7.5 meters.
- **Point C**: A flat section following the loop.
- **Height (h)**: The maximum vertical height from the ground to Point A, which needs determining.
- The total vertical distance from the base to the maximum height of the track is denoted as 20 meters.

#### Problem Statement:

The roller coaster car has a mass of 159 kg and a speed of 3 m/s at Point A. The task is to determine the minimal height (h) for the starting point A if the track is designed so that the car does not leave the track at Point B.

This is a classic problem in physics, involving concepts of energy conservation and dynamics, where the potential and kinetic energy at different points on the track determine the minimum height required at the starting point.

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