A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.2 m/s. The car is a distance d away. The bear is 29 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?
To find the maximum possible value for d, we need to determine the time it takes for the bear to catch up to the tourist.
Let's assume that the bear catches up to the tourist at point B, which is d meters away from the car.
The bear's speed is 6.0 m/s, and the tourist's speed is 4.2 m/s, so the relative speed between the bear and the tourist is 6.0 m/s - 4.2 m/s = 1.8 m/s.
Therefore, the time it takes for the bear to catch up to the tourist is t = 29 m / 1.8 m/s = 16.11 s (rounded to two decimal places).
During this time, the tourist's distance from the car can be calculated as follows:
distance = speed * time
d = 4.2 m/s * 16.11 s
d ≈ 67.67 m
So the maximum possible value for d is approximately 67.67 meters.
To find the maximum possible value for d, we need to determine the time it takes for the tourist to reach the car while being chased by the bear.
Let's analyze the situation:
The tourist is running at a speed of 4.2 m/s, while the bear is running at a speed of 6.0 m/s.
The distance between the tourist and the bear is 29 meters.
The time it takes for the tourist to reach the car is the same as the time it takes for the bear to catch up to the tourist.
Let t be the time it takes for the bear to catch up to the tourist.
During this time, the tourist will have covered a distance of 4.2t, while the bear will have covered a distance of 6.0t.
Since they meet at the car, the total distance covered by both the tourist and the bear is d.
Using the formula: distance = speed × time, we can set up the following equation:
4.2t + 29 = 6.0t
Now, we can solve for t:
4.2t - 6.0t = -29
-1.8t = -29
t = 16.11 seconds (rounded to two decimal places)
Now, we can calculate the maximum possible value for d:
d = 4.2t
d = 4.2 × 16.11
d = 67.73 meters
Therefore, the maximum possible value for d is approximately 67.73 meters.
68 m
Distance tourist = d
Distance bear = (d+29)
time the same
time = distance/speed
d/4.2 = (d+29)/6
6 d = 4.2 (d+29)
You take it from there.