Trying to escape his pursuers, a secret agent skis off a slope inclin 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 60 m (not to scale) 140 m 사
Trying to escape his pursuers, a secret agent skis off a slope inclin 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 60 m (not to scale) 140 m 사
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Find the time the skier takes to reach the position 140m below the edge
![### Problem Statement
A secret agent, in an attempt to evade pursuers, skis off a slope inclined at an angle of 30° below the horizontal at a speed of 60 km/h. The agent needs to survive by landing on snow located 140 meters below the point where he skis off the slope. To reach safety, the agent must clear a gorge that is 60 meters wide. Will the agent make it? Assume that air resistance is negligible.
### Explanation with Diagram
In the accompanying diagram (not to scale):
- The slope is shown, inclined 30° below the horizontal.
- The agent is depicted skiing off this slope.
- The edge of the slope is clearly marked.
- The horizontal distance that needs to be cleared is 60 meters.
- The vertical drop to the landing area is 140 meters.
- The initial velocity \( v_0 \) with which the agent leaves the slope is illustrated.
This problem involves the concepts of projectile motion, where the initial velocity and angle of inclination determine the horizontal and vertical displacement.
### Key Variables and Known Values
- Initial velocity, \( v_0 = 60 \) km/h (which needs to be converted to meters per second).
- Angle of inclination, \( \theta = 30° \).
- Horizontal distance (range) that must be cleared, \( R = 60 \) meters.
- Vertical distance (height) to the landing area, \( h = 140 \) meters.
### Steps to Determine if the Agent Makes It
1. **Convert the initial velocity to meters per second:**
\[
60 \, \text{km/h} = \frac{60 \times 1000}{3600} \, \text{m/s} = 16.67 \, \text{m/s}
\]
2. **Resolve the initial velocity into horizontal (\( v_{0x} \)) and vertical (\( v_{0y} \)) components:**
\[
v_{0x} = v_0 \cos \theta = 16.67 \cos 30° = 16.67 \times \frac{\sqrt{3}}{2} = 14.43 \, \text{m/s}
\]
\[
v_{0y} = v_0 \sin \theta = 16.67 \sin 30° = 16.67 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd721da83-b4b0-4147-870c-79c150dacba8%2F35743e27-d118-4f0f-9620-26258b53e969%2F4j9si6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A secret agent, in an attempt to evade pursuers, skis off a slope inclined at an angle of 30° below the horizontal at a speed of 60 km/h. The agent needs to survive by landing on snow located 140 meters below the point where he skis off the slope. To reach safety, the agent must clear a gorge that is 60 meters wide. Will the agent make it? Assume that air resistance is negligible.
### Explanation with Diagram
In the accompanying diagram (not to scale):
- The slope is shown, inclined 30° below the horizontal.
- The agent is depicted skiing off this slope.
- The edge of the slope is clearly marked.
- The horizontal distance that needs to be cleared is 60 meters.
- The vertical drop to the landing area is 140 meters.
- The initial velocity \( v_0 \) with which the agent leaves the slope is illustrated.
This problem involves the concepts of projectile motion, where the initial velocity and angle of inclination determine the horizontal and vertical displacement.
### Key Variables and Known Values
- Initial velocity, \( v_0 = 60 \) km/h (which needs to be converted to meters per second).
- Angle of inclination, \( \theta = 30° \).
- Horizontal distance (range) that must be cleared, \( R = 60 \) meters.
- Vertical distance (height) to the landing area, \( h = 140 \) meters.
### Steps to Determine if the Agent Makes It
1. **Convert the initial velocity to meters per second:**
\[
60 \, \text{km/h} = \frac{60 \times 1000}{3600} \, \text{m/s} = 16.67 \, \text{m/s}
\]
2. **Resolve the initial velocity into horizontal (\( v_{0x} \)) and vertical (\( v_{0y} \)) components:**
\[
v_{0x} = v_0 \cos \theta = 16.67 \cos 30° = 16.67 \times \frac{\sqrt{3}}{2} = 14.43 \, \text{m/s}
\]
\[
v_{0y} = v_0 \sin \theta = 16.67 \sin 30° = 16.67 \times
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