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.

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**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.
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