Question

The formula v= √2.7r models the maximum safe speed, v, in miles per hour, at which a car can travel on a curved road with radius of curvature r, in feet. A highway crew measures the radius of curvature at an exit ramp on a highway as 590 feet. What is the maximum safe speed?

For this problem, round your answer DOWN to the nearest whole number. (Think: Why is this type of rounding appropriate for this scenario?)
max safe speed= ____________

Answer 1

The maximum safe speed for a car on a curved road with a radius of curvature of 590 feet is 39 miles per hour.

Step-by-step explanation:

The formula v= √2.7r represents the maximum safe speed, v, at which a car can travel on a curved road with a radius of curvature r. To find the maximum safe speed, we need to substitute the given radius of curvature, which is 590 feet, into the formula. So, v = √2.7(590). Evaluating this expression, we get v = √1593 = 39.91 miles per hour. When rounding down to the nearest whole number, we get the maximum safe speed of 39 miles per hour. Rounding down is appropriate in this scenario because it ensures a conservative estimate of the maximum safe speed. By rounding down, we prioritize safety by allowing for a margin of error and ensuring that the car operates at a speed that will not surpass the limits of the curved road.