Chapter 02, Problem 09
A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 6.04 m/s. The car is a distance d away. The bear is 28.8 m behind the tourist and running at 7.26 m/s. The tourist reaches the car safely. What is the maximum possible value for d?
d/6.04=(d+28.8)/7.26
To find the maximum possible value for d, we need to consider the scenario where the tourist reaches the car just as the bear catches up to him.
Let's break down the problem:
1. The tourist is running towards his car at a speed of 6.04 m/s.
2. The bear is chasing the tourist from behind at a speed of 7.26 m/s.
3. The bear is initially 28.8 m behind the tourist.
4. We want to find the maximum possible value for d, the distance between the tourist's starting position and his car.
To solve this problem, we need to determine how long it takes for the bear to catch up to the tourist:
1. We can calculate the relative speed between the tourist and the bear by subtracting their speeds: 7.26 m/s - 6.04 m/s = 1.22 m/s.
2. Now, we can calculate the time it takes for the bear to catch up to the tourist by dividing the initial distance between them by the relative speed: 28.8 m / 1.22 m/s = 23.6393 seconds.
Since the tourist and the bear have the same running time, the maximum possible value for d would be the distance the tourist can run in 23.6393 seconds:
d = (runnig speed of the tourist) × (time it takes for the bear to catch up)
d = 6.04 m/s × 23.6393 s ≈ 142.9049 m
Therefore, the maximum possible value for d is approximately 142.9049 meters.