What is the maximum width of the gorge in meters so the agent clears it
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What is the maximum width of the gorge in meters so the agent clears it
Transcribed Image Text:**Problem 4:**
A secret agent skis off a slope inclined at \( \theta = 31.8 \) degrees below horizontal at a speed of \( v_0 = 17.4 \, \text{m/s} \). He must clear a gorge, and the slope on the other side of the gorge is \( h = 14.6 \, \text{m} \) below the edge of the upper slope.
**Diagram Explanation:**
The diagram on the right illustrates the skiing scenario. It shows the secret agent skiing down an inclined slope. The slope is marked with an angle \( \theta \), representing the inclination of the slope below the horizontal. The skier is depicted with a trajectory aimed across a gorge.
Key elements in the diagram include:
- **Initial Speed (\(v_0\))**: The skier begins at a speed of 17.4 m/s.
- **Angle (\( \theta \))**: The slope has an inclination of 31.8 degrees below the horizontal.
- **Height Difference (\( h \))**: The slope on the opposite side of the gorge is 14.6 meters below the starting point.
- **Horizontal Distance (\( w \))**: Represents the width of the gorge that the agent needs to clear.
This problem involves analyzing the motion and trajectory of the skier, considering initial velocity, angle of incline, and height differences to ensure safe passage across the gorge.
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