To help with vehicle stability, the outer edge of a road in a curve is raised with respect to the inner edge. This is called superelevation and is specified as the difference in elevation divided by the width of the road. It needs to be higher for faster speeds and sharper curves.The radius of a curve is the radius of the section of a circle along the middle of the road where the curve is constant. See Figure 1 for a drawing of this.Figure 1: Section of a circle along the middle of a road with radius 𝑅.In some cases the curve may need a lower speed limit than straight portions of the road. The superelevation shouldn’t be more than about .12 to keep vehicles from sliding off the road in slippery conditions.Your job is to calculate the maximum speed on a curve given the radius of the curve and the superelevation.The maximum speed is given by this formula:𝑉=(𝑅∗(𝑆+.16))/.067,where 𝑉 is the max speed in miles per hour, 𝑅 is the radius of the curve in feet, and S is the superelevation.InputThe input is a series of lines terminated by end-of-file. Each line will be a test case consisting of 𝑅 and 𝑆 separated by whitespace. 𝑅 will be an integer greater than 99 and less than 5281 and 𝑆 will be a real number greater than .009 and less than 1.0. Neither will have leading zeros. There are at most 100 lines in input.OutputFor each test case output the maximum speed rounded to the nearest integer. It is guaranteed the answer before rounding will not be within 10−3 of a half-integer value.Sample Input 1 Sample Output 11433 .091433 .122000 .09600 .1273778650
Question
To help with vehicle stability, the outer edge of a road in a curve is raised with respect to the inner edge. This is called superelevation and is specified as the difference in elevation divided by the width of the road. It needs to be higher for faster speeds and sharper curves.The radius of a curve is the radius of the section of a circle along the middle of the road where the curve is constant. See Figure 1 for a drawing of this.Figure 1: Section of a circle along the middle of a road with radius 𝑅.In some cases the curve may need a lower speed limit than straight portions of the road. The superelevation shouldn’t be more than about .12 to keep vehicles from sliding off the road in slippery conditions.Your job is to calculate the maximum speed on a curve given the radius of the curve and the superelevation.The maximum speed is given by this formula:𝑉=(𝑅∗(𝑆+.16))/.067,where 𝑉 is the max speed in miles per hour, 𝑅 is the radius of the curve in feet, and S is the superelevation.InputThe input is a series of lines terminated by end-of-file. Each line will be a test case consisting of 𝑅 and 𝑆 separated by whitespace. 𝑅 will be an integer greater than 99 and less than 5281 and 𝑆 will be a real number greater than .009 and less than 1.0. Neither will have leading zeros. There are at most 100 lines in input.OutputFor each test case output the maximum speed rounded to the nearest integer. It is guaranteed the answer before rounding will not be within 10−3 of a half-integer value.Sample Input 1 Sample Output 11433 .091433 .122000 .09600 .1273778650
Solution
To solve this problem, you need to follow these steps:
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Read the input values for 𝑅 and 𝑆. These values are separated by whitespace and each line represents a test case. The input ends when there are no more lines to read.
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For each test case, calculate the maximum speed 𝑉 using the formula 𝑉=(𝑅∗(𝑆+.16))/.067. Here, 𝑅 is the radius of the curve in feet and S is the superelevation.
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Round the calculated speed to the nearest integer. The problem guarantees that the answer before rounding will not be within 10−3 of a half-integer value.
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Output the rounded speed for each test case.
Here is a Python code snippet that implements these steps:
import sys
for line in sys.stdin:
R, S = map(float, line.split())
V = (R * (S + .16)) / .067
print(round(V))
This code reads each line from the standard input, splits it into 𝑅 and 𝑆 values, calculates the maximum speed 𝑉, and then prints the rounded speed.
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