4. A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m-high rise as shown Below. Find her final speed as she arrives at the top, given that the coefficient of friction between her skis and the snow is 0.0800. (Hint: Find the length of the incline assuming a straight-line path,as shown) V = ? KE; 2.5 m 35° Show all steps: First, how basic equations used, then insert data, then show solution for requested unknown quantities.

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### Problem 4

A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m-high rise as shown below. Find her final speed as she arrives at the top, given that the coefficient of friction between her skis and the snow is 0.0800. (Hint: Find the length of the incline assuming a straight-line path, as shown).

#### Diagram Description

- **Skier Illustration**: A skier is shown at the base of an incline. 
- **Initial Speed (\(v_i\))**: Arrow indicating initial speed of 12.0 m/s.
- **Incline Angle**: 35° angle marked at the start of the incline.
- **Height (\(h\))**: Vertical height of the incline is marked as 2.5 meters.
- **Final Speed (\(v_f\))**: Arrow indicating the final speed at the top of the incline, marked with a question mark.

### Instructions

1. **Show all steps**: 
   - Present the basic equations used for the calculations.
   - Insert the given data.
   - Solve for the requested unknown quantities.

### Solution Steps

To solve this problem, apply the principles of energy conservation and account for friction:

1. **Energy Conservation**: Consider the conversion of kinetic energy to potential energy along with the work done against friction.
   
2. **Basic Equations**:
   - **Kinetic Energy (KE)**: \( KE = \frac{1}{2} m v^2 \)
   - **Potential Energy (PE)**: \( PE = mgh \)
   - **Work done against friction (W_f)**: \( W_f = \text{friction force} \times \text{distance} \)

3. **Friction Force Calculation**: Use the coefficient of friction to calculate the frictional force.

4. **Solve for Final Speed (\(v_f\))**:
   - Use the energy relations to find \(v_f\) considering all forces and motions involved.

This approach involves substituting the given values and solving the equations step-by-step to find the final speed at the top of the incline.
Transcribed Image Text:### Problem 4 A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-m-high rise as shown below. Find her final speed as she arrives at the top, given that the coefficient of friction between her skis and the snow is 0.0800. (Hint: Find the length of the incline assuming a straight-line path, as shown). #### Diagram Description - **Skier Illustration**: A skier is shown at the base of an incline. - **Initial Speed (\(v_i\))**: Arrow indicating initial speed of 12.0 m/s. - **Incline Angle**: 35° angle marked at the start of the incline. - **Height (\(h\))**: Vertical height of the incline is marked as 2.5 meters. - **Final Speed (\(v_f\))**: Arrow indicating the final speed at the top of the incline, marked with a question mark. ### Instructions 1. **Show all steps**: - Present the basic equations used for the calculations. - Insert the given data. - Solve for the requested unknown quantities. ### Solution Steps To solve this problem, apply the principles of energy conservation and account for friction: 1. **Energy Conservation**: Consider the conversion of kinetic energy to potential energy along with the work done against friction. 2. **Basic Equations**: - **Kinetic Energy (KE)**: \( KE = \frac{1}{2} m v^2 \) - **Potential Energy (PE)**: \( PE = mgh \) - **Work done against friction (W_f)**: \( W_f = \text{friction force} \times \text{distance} \) 3. **Friction Force Calculation**: Use the coefficient of friction to calculate the frictional force. 4. **Solve for Final Speed (\(v_f\))**: - Use the energy relations to find \(v_f\) considering all forces and motions involved. This approach involves substituting the given values and solving the equations step-by-step to find the final speed at the top of the incline.
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