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.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fe4c5ff-3153-480d-9c91-a45f42309b22%2F931b2133-6358-4b8e-80c7-b842f94cb960%2Fvood7es.jpeg&w=3840&q=75)

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