A tourist being chased by an angry bear is running in a...

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.0 $\mathrm{m} / \mathrm{s}$ . The car is a distance $d$ away. The bear is 26 $\mathrm{m}$ behind the tourist and running at 6.0 $\mathrm{m} / \mathrm{s}$ . The tourist reaches the car safely. What is the maximum possible value for $d ?$

Key Concepts

Pursuit Problem Analysis

Pursuit problems involve scenarios where one entity is chasing another, and they require setting up equations that relate the time taken by both parties to cover certain distances. The key is to determine the moment when the pursuer catches the target, which typically involves equating the expressions for distance traveled by both and solving for time or distance. This analysis is essential in determining safety or catch conditions in dynamic chase scenarios.

Relative Velocity

Relative velocity is the measure of how fast one object is moving compared to another. In pursuit problems, it helps in understanding how quickly the gap between the pursuer and the target is closing. By considering the speeds of both objects and their initial separation, one can establish the conditions under which one object might catch up to or fall behind the other.

Uniform Motion

Uniform motion refers to the type of motion in which an object travels at a constant speed in a straight line. In such cases, the relationship between distance, speed, and time is linear, allowing one to calculate any one of these variables when the other two are known. This concept is fundamental in solving problems where acceleration is zero, as it simplifies the analysis of an object’s trajectory over time.

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