The stopping distance d of an automobile is directly proportional to the square of its speed s . On a road surface, a car requires $78$ feet to stop when its speed is $25$ miles per hour. The brakes are applied when the car is traveling at $30$ miles per hour under similar road conditions. Estimate the stopping distance to the nearest foot.

A) $123.5$ feet
B) $178.2$ feet
C) $112.3$ feet
D) $3.7$ feet
E) $101.1$ feet

We know that stopping distance, d is directly proportional to the square of speed, s. This can be written as:

d=k*s^2

where k is the constant of proportionality.

To find k, we can use the given information that the car requires 78 feet to stop when its speed is 25 miles per hour:

78=k*25^2
k=78/625
k=0.1248

Now we can use this value of k to estimate the stopping distance when the car is traveling at 30 miles per hour:

d=0.1248*30^2
d=112.3 feet

Therefore, the answer is C, 112.3 feet, rounded to the nearest foot.