Question

When a driver slams the brakes on a car, the length of skid marks on the road varies directly with the square of the speed of the car. At 45 mph the skid mark 90 feet long. How long are the skid makes if the car is traveling at 30 mph?

Answer 1

Let's call the length of skid marks "L" and the speed of the car "S". From the information given, we have:

L = k * S^2 (where k is some constant of proportionality)

At 45 mph, L = 90 feet, so we can substitute:

90 = k * 45^2

Solving for k, we find:

k = 90 / 45^2 = 0.0044

Now that we know k, we can find the length of the skid marks at 30 mph:

L = 0.0044 * 30^2 = 26.4 feet

So the skid marks are 26.4 feet long at 30 mph.

Hope this helps!