The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car travelling 70mph can stop in 270ft, how many feet will it take the same car to stop when it is travelling 60mph?
Thank you.
To solve this problem, we're given that the stopping distance (d) varies directly with the square of the speed (r). This means that we can write an equation in the form d = k * r^2, where k is a constant of proportionality.
We can use the given information to find the value of k. We know that when the car is traveling at 70mph, it can stop in 270ft. So we have the following equation:
270 = k * 70^2
To find the value of k, we can solve for it:
k = 270 / (70^2)
k = 270 / 4900
k ≈ 0.0551
Now that we have the value of k, we can use it to find the stopping distance when the car is traveling at 60mph. We can use the equation d = k * r^2 and substitute r = 60:
d = 0.0551 * 60^2
d = 0.0551 * 3600
d ≈ 198.36
Therefore, it will take approximately 198.36 feet for the same car to stop when it is traveling at 60mph.