A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 5.56 m/s. The car is a distance d away. The bear is 26.6 m behind the tourist and running at 7.69 m/s. The tourist reaches the car safely. What is the maximum possible value for d?
tourist runs d at 5.56
bear runs (d+26.6) at 7.69
same time for both
time =
(d+26.6)/7.69 = d/5.56
solve for d
To find the maximum possible value for d, we need to consider the time it will take for the bear to catch up to the tourist.
Let's assume the time it takes for the bear to catch up to the tourist is t seconds.
The distance traveled by the tourist is given by:
distance = speed × time
distance = 5.56 m/s × t
The distance traveled by the bear is given by:
distance = speed × time
distance = 7.69 m/s × (t + 26.6 m)
We add 26.6 m to account for the initial distance between the bear and the tourist.
Since the tourist reaches the car safely, the distance traveled by the tourist must be more than the distance traveled by the bear.
Therefore, we can set up the following equation:
5.56 m/s × t > 7.69 m/s × (t + 26.6 m)
Now, let's solve this inequality to find the maximum value for t, which will give us the maximum value for d.
5.56 m/s × t > 7.69 m/s × (t + 26.6 m)
Expanding the right-hand side:
5.56 m/s × t > 7.69 m/s × t + 7.69 m/s × 26.6 m
Combining like terms:
5.56 m/s × t – 7.69 m/s × t > 7.69 m/s × 26.6 m
Simplifying:
-2.13 m/s × t > 7.69 m/s × 26.6 m
Dividing both sides by -2.13 m/s (note: since we are dividing by a negative number, the inequality changes direction):
t < (7.69 m/s × 26.6 m) / -2.13 m/s
Calculating the right-hand side:
t < 96.8913 s
Since time cannot be negative, the maximum value for t is 96.8913 s.
Now we can find the maximum possible value for d, which is the distance traveled by the tourist:
d = 5.56 m/s × t
d = 5.56 m/s × 96.8913 s
d ≈ 537.992 m
Therefore, the maximum possible value for d is approximately 537.992 meters.