A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 6.54 m/s. The car is a distance d away. The bear is 26.0 m behind the tourist and running at 10.4 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 consider the scenario where the bear is closest to catching the tourist. This happens when the bear and the tourist reach the car at the same time.
Let's first calculate the time it takes for the tourist to reach the car. We can use the formula:
time = distance / speed
The distance the tourist needs to cover is d, and the speed is given as 6.54 m/s. Therefore, the time taken by the tourist to reach the car is:
time_tourist = d / 6.54
Now, let's calculate the time it takes for the bear to reach the car. The bear starts 26 m behind the tourist, and its speed is given as 10.4 m/s. Therefore, the time taken by the bear to reach the car is:
time_bear = (d + 26) / 10.4
Since we want the bear and the tourist to reach the car at the same time, the times for both should be equal:
time_tourist = time_bear
Substituting the expressions for time_tourist and time_bear:
d / 6.54 = (d + 26) / 10.4
To find the maximum possible value for d, we solve this equation for d.
Multiplying both sides of the equation by 6.54 and 10.4 to eliminate the denominators:
10.4d = 6.54(d + 26)
Expanding the equation:
10.4d = 6.54d + 170.04
Subtracting 6.54d from both sides:
3.86d = 170.04
Dividing both sides by 3.86:
d = 170.04 / 3.86
Calculating the value:
d ≈ 44.02
Hence, the maximum possible value for d is approximately 44.02 meters.