A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 5.95 m/s. The car is a distance d away. The bear is 37.0 m behind the tourist and running at 7.80 m/s. The tourist reaches the car safely. What is the maximum possible value for d?

L=37 m

v₁=5.95 m/s
v₂=7.8 m/s
L+ v₁t= v₂t
t=L/ (v₂-v₁)=
=37/(7.8-5.95) =20 s
d= v₁t=5.95•20=119 m.

To find the maximum possible value for d, we need to determine the condition where the bear and the tourist reach the car simultaneously.

Let's analyze the situation:
1. The tourist is running towards the car at a speed of 5.95 m/s, and the bear is running behind the tourist at a speed of 7.80 m/s.
2. The bear is initially 37.0 m behind the tourist.

Since the bear is faster, it will catch up to the tourist eventually. The time it takes for the bear to catch up to the tourist can be calculated using the formula:

time = distance / speed

Let's calculate the time it takes for the bear to catch up to the tourist:
time = 37.0 m / (7.80 m/s - 5.95 m/s)
time = 37.0 m / 1.85 m/s
time ≈ 20 seconds

Now, since the tourist reaches the car safely, the bear and the tourist should reach the car simultaneously. The distance the tourist runs in 20 seconds can be calculated using:

distance = speed × time
distance = 5.95 m/s × 20 s
distance = 119 m

Therefore, the maximum possible value for d is 119 m, as the tourist can safely reach the car before the bear catches up.