A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.24 m/s. The car is a distance d away. The bear is 31.1 m behind the tourist and running at 4.50 m/s. The tourist reaches the car safely. What is the maximum possible value for d?
To answer this question, we need to determine the maximum possible distance (d) between the tourist and his car. We can do this by finding the time it takes for the bear to catch up to the tourist and then using that time to calculate the maximum distance.
Let's start by finding the time it takes for the bear to catch up to the tourist. We can use the formula:
time = distance / speed.
The distance traveled by the tourist is the distance between him and his car, which is d. The distance traveled by the bear is the initial distance between the bear and the tourist, which is 31.1m. The speeds are 3.24 m/s for the tourist and 4.50 m/s for the bear.
So, the time it takes for the bear to catch up to the tourist is:
time = 31.1 m / (4.50 m/s - 3.24 m/s) = 31.1 m / 1.26 m/s = 24.6 s.
Now that we have the time it takes for the bear to catch up to the tourist, we can determine the maximum distance (d) between the tourist and his car. We use the formula:
distance = speed × time.
The speed of the tourist is 3.24 m/s, and the time is 24.6 s.
distance = 3.24 m/s × 24.6 s = 79.904 m.
Therefore, the maximum possible value for d, the distance between the tourist and his car, is approximately 79.904 meters.
To find the maximum possible value for d, we need to determine the time it takes for the bear to catch up with the tourist.
Let's assume that the bear catches up with the tourist at time t. At that time, the distance the tourist travels is equal to the distance the bear travels, plus the distance between them:
Distance traveled by the tourist = Distance traveled by the bear + Distance between them
Using the equation: distance = speed x time
3.24t = 4.50t + 31.1
Rearranging the equation:
3.24t - 4.50t = 31.1
Simplifying:
-1.26t = 31.1
Dividing both sides by -1.26:
t = -31.1 / -1.26
t ≈ 24.6 seconds
This means that it takes approximately 24.6 seconds for the bear to catch up with the tourist.
Now, to find the maximum possible value for d, we need to calculate the distance the tourist travels during this time:
Distance = speed x time
Distance = 3.24 m/s x 24.6 s
Distance ≈ 79.6 meters
Therefore, the maximum possible value for d is approximately 79.6 meters.
This is not Physics.
tourist runs distance d
bear runs distance (d+31.1)
same time t
d = 3.24 t
d+31.1 = 4.5 t
so
d + 31.1 = 4.5(d/3.24)
3.24 d + 100.7 = 4.5 d
d = 80 meters max
this tourist is no track star :(