A boy shoves his stuffed toy zebra down a frictionless chute. It starts at a height of 1.83 m above the bottom of the chute with an initial speed of 1.65 m/s. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with a coefficient of kinetic friction of 0.203. How far from the bottom of the chute does the toy zebra come to rest? Assume g = 9.81 m/s².
A boy shoves his stuffed toy zebra down a frictionless chute. It starts at a height of 1.83 m above the bottom of the chute with an initial speed of 1.65 m/s. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with a coefficient of kinetic friction of 0.203. How far from the bottom of the chute does the toy zebra come to rest? Assume g = 9.81 m/s².
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
Transcribed Image Text:### Problem Description
A boy shoves his stuffed toy zebra down a frictionless chute. It starts at a height of 1.83 m above the bottom of the chute with an initial speed of 1.65 m/s. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with a coefficient of kinetic friction of 0.203. How far from the bottom of the chute does the toy zebra come to rest? Assume \( g = 9.81 \, \text{m/s}^2 \).
### Solution
**Answer:**
The toy zebra comes to rest at a distance of 8.9605 meters from the bottom of the chute.
### Explanation
1. **Initial Conditions:**
- Height of the chute: 1.83 m
- Initial speed at the top: 1.65 m/s
2. **Friction on the Horizontal Surface:**
- Coefficient of kinetic friction: 0.203
3. **Physics Application:**
- As the toy comes down the chute, gravitational potential energy is converted into kinetic energy.
- When reaching the horizontal surface, the kinetic energy is reduced due to the work done against friction until the toy comes to a stop.
### Diagram Description
(No diagrams are present in the image to describe, but one could imagine a simple side view of a chute leading to a horizontal surface.)
### Additional Notes
- For a comprehensive understanding, one could apply energy conservation principles and the work-energy theorem.
- Potential energy at the top = Kinetic energy at the bottom + Work done against friction.
- This example illustrates the transition from potential to kinetic energy, and the role of friction in kinetic motion.
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