1. Alice is about to sled down a snow-covered hill as shown below. The hill is so slippery that there's no friction between her sled and the snow. What will Alice's acceleration down the hill be? (Hint: Anything close to the earth's surface that falls freely will acceleration straight downward at a constant gravitational acceleration, g. Find the component of this gravitational acceleration that is parallel with the surface of the hill. Be sure to draw a large diagram that shows the vector g and how you're finding the parallel component.)
1. Alice is about to sled down a snow-covered hill as shown below. The hill is so slippery that there's no friction between her sled and the snow. What will Alice's acceleration down the hill be? (Hint: Anything close to the earth's surface that falls freely will acceleration straight downward at a constant gravitational acceleration, g. Find the component of this gravitational acceleration that is parallel with the surface of the hill. Be sure to draw a large diagram that shows the vector g and how you're finding the parallel component.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This is for my Precalc class. Course covers trigonometric, polynomial, and rational functions and their applications.
#### Diagram Explanation:
The diagram depicts Alice sitting on a sled, preparing to slide down a hill inclined at an angle θ. The angle θ is the angle between the hill’s surface and the horizontal ground.
#### Solution Steps:
1. **Identify the Gravitational Force (g):**
- The gravitational force acts vertically downward with an acceleration \( g \approx 9.8 \, \text{m/s}^2 \).
2. **Resolve the Gravitational Force into Components:**
- The gravitational force \( g \) can be resolved into two components:
- A component perpendicular to the hill’s surface.
- A component parallel to the hill’s surface (which causes the sled to accelerate down the hill).
3. **Calculate the Parallel Component:**
- The parallel component of the gravitational force causing Alice to slide down the hill can be found using:
\[ g_{\parallel} = g \sin(\theta) \]
where \( \sin(\theta) \) is the sine of the angle of the hill’s incline.
4. **Resultant Acceleration:**
- Since there is no friction, the parallel component of gravity is the net acceleration of Alice down the hill:
\[ a = g \sin(\theta) \]
---
By following these steps, Alice's acceleration down the hill can be determined considering the given conditions and the absence of friction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ed55e1d-e879-4c65-8f78-0d2ec6e81dd9%2F8e14ae96-2941-4c7f-b902-3bb23d4087d3%2F8bfjce_processed.png&w=3840&q=75)
Transcribed Image Text:### Physics Problem: Acceleration Down a Hill
---
#### Problem Statement:
1. Alice is about to sled down a snow-covered hill as shown below. The hill is so slippery that there’s no friction between her sled and the snow. What will Alice’s acceleration down the hill be? (*Hint: Anything close to the earth’s surface that falls freely will accelerate straight downward at a constant gravitational acceleration, g. Find the component of this gravitational acceleration that is parallel with the surface of the hill. Be sure to draw a large diagram that shows the vector g and how you’re finding the parallel component.*)
#### Diagram Explanation:
The diagram depicts Alice sitting on a sled, preparing to slide down a hill inclined at an angle θ. The angle θ is the angle between the hill’s surface and the horizontal ground.
#### Solution Steps:
1. **Identify the Gravitational Force (g):**
- The gravitational force acts vertically downward with an acceleration \( g \approx 9.8 \, \text{m/s}^2 \).
2. **Resolve the Gravitational Force into Components:**
- The gravitational force \( g \) can be resolved into two components:
- A component perpendicular to the hill’s surface.
- A component parallel to the hill’s surface (which causes the sled to accelerate down the hill).
3. **Calculate the Parallel Component:**
- The parallel component of the gravitational force causing Alice to slide down the hill can be found using:
\[ g_{\parallel} = g \sin(\theta) \]
where \( \sin(\theta) \) is the sine of the angle of the hill’s incline.
4. **Resultant Acceleration:**
- Since there is no friction, the parallel component of gravity is the net acceleration of Alice down the hill:
\[ a = g \sin(\theta) \]
---
By following these steps, Alice's acceleration down the hill can be determined considering the given conditions and the absence of friction.
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