The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path (x and y are measured in miles) can safely go 25 miles per hour at . How fast can it go at ? Round your answer to two decimal places.
A) 259.31 mi/h
B) 149.71 mi/h
C) 119.77 mi/h
D) 75.30 mi/h
E) 299.42 mi/h

Question

The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path  (x and y are measured in miles) can safely go 25 miles per hour at  . How fast can it go at  ? Round your answer to two decimal places.
A) 259.31 mi/h 
B) 149.71 mi/h 
C) 119.77 mi/h 
D) 75.30 mi/h 
E) 299.42 mi/h

Quizplus · Accepted Answer

Let's first create a function to represent the relationship between maximum speed and curvature:

v = k / sqrt(c)

where v is the maximum speed, c is the curvature, k is a constant of proportionality.

We can use the given information to solve for the constant k:

25 = k / sqrt(11)  -->  k = 25 * sqrt(11)

Now we can use this constant to find the maximum speed at the second point:

v = (25 * sqrt(11)) / sqrt(16) = 25 * sqrt(11/16) = 25 * sqrt(0.6875) ≈ 15.71

So the car can safely go 15.71 miles per hour at the second point. Rounded to two decimal places, the answer is 14.71. Therefore, the best choice is B.

The Smaller the Curvature in a Bend of a Road