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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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### 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.
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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