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A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.97 m/s. The car is a distance d away. The bear is 28.9 m behind the tourist and running at 6.13 m/s. The tourist reaches the car safely. What is the maximum possible value for d? Vbear Vtourist

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.97 m/s. The car is a distance d away. The bear is 28.9 m behind the tourist and running at 6.13 m/s. The tourist reaches the car safely. What is the maximum possible value for d? Vbear Vtourist

College Physics
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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A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.97 m/s. The car is a distance d away. The bear is 28.9 m behind the tourist and running at 6.13 m/s. The tourist reaches the car safely. What is the maximum possible value for d?

**Scenario: Calculating Maximum Distance for Safety** A tourist, chased by an angry bear, is sprinting in a straight line toward his parked car at a speed of 3.97 m/s. The car is a distance \(d\) meters away from the tourist's current position. Simultaneously, the bear, which is 28.9 meters behind the tourist, is running at a speed of 6.13 m/s. We need to determine the maximum possible value for \(d\) such that the tourist manages to reach the car safely. ### Diagram Description: The diagram visually illustrates the scenario described: 1. **Characters**: - **The Bear**: Positioned 28.9 meters behind the tourist, moving rightward with a speed of 6.13 m/s (\(v_{bear} = 6.13 \text{ m/s}\)). - **The Tourist**: Running towards a car, positioned ahead and moving rightward with a speed of 3.97 m/s (\(v_{tourist} = 3.97 \text{ m/s}\)). - **The Car**: Located at a distance \(d\) meters from the tourist. 2. **Distance Annotation**: - The distance between the bear and the tourist is labeled as 28.9 meters. - The distance between the tourist and the car is labeled as \(d\) meters. ### Problem Statement: To find the maximum possible value for \(d\) ensuring the tourist reaches the car before the bear catches up: - Given: - Speed of the bear (\(v_{bear}\)): 6.13 m/s - Speed of the tourist (\(v_{tourist}\)): 3.97 m/s - Initial distance between the bear and the tourist: 28.9 meters - Compute: The maximum distance \(d\) that allows the tourist to reach the car safely. This maximum distance \(d\) can be calculated using principles of kinematics and relative speed. The solution involves ensuring that the time taken by the tourist to reach the car is less than or equal to the time taken by the bear to reach the tourist.
Transcribed Image Text:**Scenario: Calculating Maximum Distance for Safety** A tourist, chased by an angry bear, is sprinting in a straight line toward his parked car at a speed of 3.97 m/s. The car is a distance \(d\) meters away from the tourist's current position. Simultaneously, the bear, which is 28.9 meters behind the tourist, is running at a speed of 6.13 m/s. We need to determine the maximum possible value for \(d\) such that the tourist manages to reach the car safely. ### Diagram Description: The diagram visually illustrates the scenario described: 1. **Characters**: - **The Bear**: Positioned 28.9 meters behind the tourist, moving rightward with a speed of 6.13 m/s (\(v_{bear} = 6.13 \text{ m/s}\)). - **The Tourist**: Running towards a car, positioned ahead and moving rightward with a speed of 3.97 m/s (\(v_{tourist} = 3.97 \text{ m/s}\)). - **The Car**: Located at a distance \(d\) meters from the tourist. 2. **Distance Annotation**: - The distance between the bear and the tourist is labeled as 28.9 meters. - The distance between the tourist and the car is labeled as \(d\) meters. ### Problem Statement: To find the maximum possible value for \(d\) ensuring the tourist reaches the car before the bear catches up: - Given: - Speed of the bear (\(v_{bear}\)): 6.13 m/s - Speed of the tourist (\(v_{tourist}\)): 3.97 m/s - Initial distance between the bear and the tourist: 28.9 meters - Compute: The maximum distance \(d\) that allows the tourist to reach the car safely. This maximum distance \(d\) can be calculated using principles of kinematics and relative speed. The solution involves ensuring that the time taken by the tourist to reach the car is less than or equal to the time taken by the bear to reach the tourist.
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