The stopping distance of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 80 mph can stop in 360ft, how many feet will it take the same car to stoop when its traveling 50 mph?

d = k r^2

360 = k (80)^2
k = 360/80^2

d = [360/80^2] * 50^2

d = 360 (25/64)

d = 141 ft

To solve this problem, we can use the concept of direct variation. The stopping distance of the car is directly proportional to the square of its speed. Let's use the variables r1 and d1 to represent the speed (in mph) and stopping distance (in feet) when the car is traveling at 80 mph. Similarly, let's use r2 and d2 to represent the speed and stopping distance when the car is traveling at 50 mph.

According to the given information:
r1 = 80 mph
d1 = 360 ft

We need to find d2, the stopping distance when the car is traveling at 50 mph.

Since the stopping distance varies directly as the square of the speed, we can write the following equation:

(d2 / d1) = (r2^2 / r1^2)

To find d2, we can rearrange the equation as follows:

d2 = (d1 * r2^2) / r1^2

Substituting the known values:
d2 = (360 * 50^2) / 80^2

Now, let's calculate d2:

d2 = (360 * 2500) / 6400
d2 = 90000 / 6400
d2 = 14.0625 (approx.)

Therefore, when the car is traveling at 50 mph, it will take approximately 14.0625 feet to stop.