The Kingda Ka is a giant among roller coasters. Located in Jackson Township, New Jersey, the ride includes a vertical drop of 127 m. Suppose that the coaster has a speed of 6.0 m/ s at the top of the drop. Neglect friction and air resistance and find the speed of the riders at the bottom.

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)...
icon
Related questions
icon
Concept explainers
Topic Video
Question
100%

Can someone do this showing the steps to get this answer 50.3 

**Roller Coaster Physics: Calculating Final Speed**

*The Kingda Ka Experience*

Kingda Ka is a giant among roller coasters. Located in Jackson Township, New Jersey, the ride includes a vertical drop of 127 meters. Suppose the coaster has a speed of 6.0 m/s at the top of the drop. Neglect friction and air resistance and find the speed of the riders at the bottom.

To solve this, use the principle of conservation of mechanical energy. You can calculate the potential and kinetic energy at the top and bottom of the drop.

Given:
- Initial speed at the top, \( v_i = 6.0 \, \text{m/s} \)
- Height of the drop, \( h = 127 \, \text{m} \)
- Gravitational acceleration, \( g = 9.81 \, \text{m/s}^2 \)

Use the equation:
\[ v_f = \sqrt{v_i^2 + 2gh} \]

Substitute the given values to find the final speed, \( v_f \).

The answer is approximately \( 50.3 \, \text{m/s} \).

This calculation demonstrates the exhilarating force of gravity on roller coasters, providing a thrill for riders through the physics of motion and energy conservation.

**Exercise Question 4:**
- Calculate the speed of a different roller coaster design with varying initial speeds and heights.
Transcribed Image Text:**Roller Coaster Physics: Calculating Final Speed** *The Kingda Ka Experience* Kingda Ka is a giant among roller coasters. Located in Jackson Township, New Jersey, the ride includes a vertical drop of 127 meters. Suppose the coaster has a speed of 6.0 m/s at the top of the drop. Neglect friction and air resistance and find the speed of the riders at the bottom. To solve this, use the principle of conservation of mechanical energy. You can calculate the potential and kinetic energy at the top and bottom of the drop. Given: - Initial speed at the top, \( v_i = 6.0 \, \text{m/s} \) - Height of the drop, \( h = 127 \, \text{m} \) - Gravitational acceleration, \( g = 9.81 \, \text{m/s}^2 \) Use the equation: \[ v_f = \sqrt{v_i^2 + 2gh} \] Substitute the given values to find the final speed, \( v_f \). The answer is approximately \( 50.3 \, \text{m/s} \). This calculation demonstrates the exhilarating force of gravity on roller coasters, providing a thrill for riders through the physics of motion and energy conservation. **Exercise Question 4:** - Calculate the speed of a different roller coaster design with varying initial speeds and heights.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Displacement, velocity and acceleration
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON