A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.7 m/s. The car is a distance d away. The bear is 27 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely. What is the maximum possible value for d?
(x+d)/v2 =d/v1
x•v1=d(v2-v1)
d=x•v1/(v2-v1)=27•3.7/(6-3.7)=43.4 m
To find the maximum possible value for d, we need to consider the scenario where the bear is closest to the tourist when he reaches the car. In this case, the bear will be right behind the tourist as he reaches the car.
Let's first find the time it takes for the tourist to reach the car. We can use the formula:
time = distance / speed
The distance that the tourist has to cover is d, and his speed is 3.7 m/s. So the time taken by the tourist to reach the car is:
time = d / 3.7
Now, let's find the distance the bear can cover in this time. The bear is 27 m behind the tourist and runs at 6.0 m/s. So the distance the bear can cover in the same time is:
distance covered by bear = speed of bear × time
distance covered by bear = 6.0 × (d / 3.7)
Since the bear is right behind the tourist, this distance covered by the bear should be equal to the distance between the bear and the tourist, which is 27 m. Therefore, we have:
6.0 × (d / 3.7) = 27
We can now solve for the value of d:
d = (27 × 3.7) / 6.0
Calculating this value gives us:
d ≈ 16.71 m
Therefore, the maximum possible value for d is approximately 16.71 meters.