The formula relating the speed of a vehicle (S, in miles per hour) that a car was traveling at the moment the brakes were applied causing the vehicle to skid to a stop, traffic investigators use the formula S = square root of 30fL, where L is the length(in feet) of the skid marks made by the tires and f is the friction coefficient (typically between 0.0 and 1.0) between the road and the tires.

(a) determine the length of the skid marks if the vehicle has a speed of 30 mph and the rather bald tires had a friction coefficient of 0.5.
(b) redo problem "A" if the vehicle has the speed of 30 mph but had better tires with the friction value of 0.75 .

what's the trouble? They say

S = √(30fL)
just plug in your numbers and solve for L

To solve this problem, we will use the formula S = √(30fL) given in the question, where S is the speed of the vehicle, L is the length of the skid marks, and f is the friction coefficient.

(a) To determine the length of the skid marks when the vehicle is traveling at 30 mph with a friction coefficient of 0.5, we substitute the given values into the formula:

S = √(30fL)
S = √(30 * 0.5 * L)
30 = √(15L)
30^2 = 15L
900 = 15L
L = 900/15
L = 60 feet

Therefore, the length of the skid marks is 60 feet.

(b) To redo the calculation with better tires having a friction coefficient of 0.75, we will use the same formula but substitute the new value of f:

S = √(30fL)
S = √(30 * 0.75 * L)
30 = √(22.5L)
30^2 = 22.5L
900 = 22.5L
L = 900/22.5
L = 40 feet

Therefore, with better tires, the length of the skid marks is 40 feet when the vehicle is traveling at 30 mph and the friction coefficient is 0.75.