a tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.0m/s. the car is d distance away. the bear is 26.0m behind the tourist and running at 6.0m/s. the tourist reaches the car safely. what is the maximum possible value for d.
To find the maximum possible value for d, we need to consider the scenario where the bear is closest to the tourist when they reach the car. Let's break down the problem and find the time it takes for the tourist to reach the car.
First, let's determine the time it takes for both the tourist and the bear to reach the car. We can use the formula:
time = distance / speed
For the tourist:
time_tourist = distance_tourist / speed_tourist
time_tourist = d / 4.0
For the bear:
time_bear = distance_bear / speed_bear
time_bear = 26.0 / 6.0
Since the bear is chasing the tourist, it will take the bear less time to cover the distance of 26.0m compared to the tourist reaching the car.
Now, let's assume the maximum possible value for d. It would occur when the bear and the tourist reach the car at the same time. So, we need to set the times equal to each other:
d / 4.0 = 26.0 / 6.0
Now let's solve for d:
d = (4.0 / 6.0) * 26.0
d = 17.33 meters (rounded to two decimal places)
Therefore, the maximum possible value for d is approximately 17.33 meters.