A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 5.31 m/s. The car is a distance d away. The bear is 18.6 m behind the tourist and running at 8.01 m/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 determine the time it takes for the tourist to reach the car and use that information to calculate the distance traveled by the bear during that time.
First, let's find the time it takes for the tourist to reach the car. We can use the formula:
time = distance / speed
The distance between the bear and the tourist is 18.6 m, and the tourist is running at a speed of 5.31 m/s. Thus, the time taken by the tourist to reach the car is:
time = 18.6 m / 5.31 m/s = 3.5 seconds.
Next, we need to calculate the distance traveled by the bear during this time. The bear is running at a speed of 8.01 m/s, and the time taken by the tourist to reach the car is 3.5 seconds. Therefore, the distance traveled by the bear is:
distance = speed × time = 8.01 m/s × 3.5 s = 28.035 m.
Since the bear was initially 18.6 m behind the tourist, the maximum possible value for d is:
d = distance traveled by the bear + initial distance between the bear and the tourist
= 28.035 m + 18.6 m
= 46.635 m.
Therefore, the maximum possible value for d is 46.635 m.