A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.55 m/s. The car is a distance d away. The bear is 17.1 m behind the tourist and running at 4.84 m/s. The tourist reaches the car safely. What is the maximum possible value for d?
Both traveled same time .
d/3.55=T
(d+17.1)/4.84=T
set them equal, solve for T.
Now, use the first equation to solve for d.
To find the maximum possible value for d, we need to determine the point where the bear catches up to the tourist.
Let's consider the relative velocity between the bear and the tourist. Since the bear is chasing the tourist, the relative velocity is the difference between their velocities:
Relative velocity = Bear's velocity - Tourist's velocity
= 4.84 m/s - 3.55 m/s
= 1.29 m/s
Now, let's determine the time it takes for the bear to catch up to the tourist:
Time = Distance / Relative velocity
The distance the bear needs to travel to catch up to the tourist is the initial separation between them, which is 17.1 m.
Time = 17.1 m / 1.29 m/s
≈ 13.26 seconds
Since the tourist reaches the car safely, this means the bear must be behind the tourist when they reach the car. We can find the distance covered by the tourist in 13.26 seconds:
Distance covered by the tourist = Tourist's velocity × Time
Distance covered by the tourist = 3.55 m/s × 13.26 s
≈ 47.07 m
Therefore, the maximum possible value for d, the distance between the car and the starting position of the tourist, is approximately 47.07 meters.