horizontal at 60 km/h. To survive and land on the snow 140 m below, he/she must clear a gorge 60 m wide. Does he/she make it? Ignore air resistance. Edge 30° Vo (not to scale) -60 m- 140 m

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Chapter1: Units, Trigonometry. And Vectors
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Calculate the x and y components of the skiers initial velocity
**Physics Problem: Skiing for Survival**

**Scenario:**
A secret agent, in an attempt to evade capture, skis off a slope inclined at 30° below the horizontal at a speed of 60 km/h. To survive and land on the snow 140 meters below, he/she must clear a gorge that is 60 meters wide. The problem requires determining if the agent will successfully make the jump, ignoring air resistance.

**Details of the Problem:**

1. **Initial Velocity (\(v_0\))**:
   - The initial speed of the agent is 60 km/h, which is equivalent to 16.67 meters per second (since 1 km/h = 1000 m/3600 s).

2. **Slope Inclination**:
   - The incline of the slope is 30° below the horizontal.

3. **Horizontal Distance to Clear**:
   - The agent must clear a horizontal distance of 60 meters.

4. **Vertical Drop**:
   - The agent will fall a vertical distance of 140 meters.

**Diagram Explanation:**
- The diagram illustrates a skier and the trajectory needed to clear the gorge.
- The skier begins at the edge of a slope that angles 30° downward.
- The initial velocity vector (\(v_0\)) is depicted, indicating the direction of travel as the skier leaves the edge.
- The vertical drop is marked as 140 meters, and the horizontal distance that needs to be cleared is labeled as 60 meters.
- The edge of the slope, the inclination angle, and the required landing point are all indicated in the diagram for clarity.

**Calculation Approach:**
To determine if the skier will make it, one must calculate the horizontal and vertical components of the skier's initial velocity and use the range equations of projectile motion. 

- **Horizontal Component of Initial Velocity ( \( v_{0x} \) )**: 
  \( v_{0x} = v_0 \cos(30°) \)
  \( v_{0x} = 16.67 \times \cos(30°) \approx 14.43 \) m/s

- **Vertical Component of Initial Velocity ( \( v_{0y} \) )**: 
  \( v_{0y} = v_0 \sin(30°) \)
  \( v_{0y} = 16.67 \times \sin(30°) \
Transcribed Image Text:**Physics Problem: Skiing for Survival** **Scenario:** A secret agent, in an attempt to evade capture, skis off a slope inclined at 30° below the horizontal at a speed of 60 km/h. To survive and land on the snow 140 meters below, he/she must clear a gorge that is 60 meters wide. The problem requires determining if the agent will successfully make the jump, ignoring air resistance. **Details of the Problem:** 1. **Initial Velocity (\(v_0\))**: - The initial speed of the agent is 60 km/h, which is equivalent to 16.67 meters per second (since 1 km/h = 1000 m/3600 s). 2. **Slope Inclination**: - The incline of the slope is 30° below the horizontal. 3. **Horizontal Distance to Clear**: - The agent must clear a horizontal distance of 60 meters. 4. **Vertical Drop**: - The agent will fall a vertical distance of 140 meters. **Diagram Explanation:** - The diagram illustrates a skier and the trajectory needed to clear the gorge. - The skier begins at the edge of a slope that angles 30° downward. - The initial velocity vector (\(v_0\)) is depicted, indicating the direction of travel as the skier leaves the edge. - The vertical drop is marked as 140 meters, and the horizontal distance that needs to be cleared is labeled as 60 meters. - The edge of the slope, the inclination angle, and the required landing point are all indicated in the diagram for clarity. **Calculation Approach:** To determine if the skier will make it, one must calculate the horizontal and vertical components of the skier's initial velocity and use the range equations of projectile motion. - **Horizontal Component of Initial Velocity ( \( v_{0x} \) )**: \( v_{0x} = v_0 \cos(30°) \) \( v_{0x} = 16.67 \times \cos(30°) \approx 14.43 \) m/s - **Vertical Component of Initial Velocity ( \( v_{0y} \) )**: \( v_{0y} = v_0 \sin(30°) \) \( v_{0y} = 16.67 \times \sin(30°) \
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