Highway curves If a circular curve without any banking has a radius of R feet, the speed limitL.in miles per hour for the curve is L=1.5 R.
(a.)Find the speed limit for a curve having a radius of 400 feet.
(b.) If the radius of a curve doubles, what happens to the speed limit?
(c.) A curve with a 40 mile per hou speed limit is being designed What should be it's radius?
(a.) To find the speed limit for a curve with a radius of 400 feet, we can substitute R = 400 into the formula L = 1.5R.
L = 1.5 * 400
L = 600
Therefore, the speed limit for a curve with a radius of 400 feet is 600 miles per hour.
(b.) If the radius of a curve doubles, let's say the new radius is 2R. We can substitute this into the formula L = 1.5R.
L = 1.5 * (2R)
L = 3R
So, if the radius doubles, the speed limit will also triple.
(c.) If a curve is designed to have a speed limit of 40 miles per hour, we can rearrange the formula L = 1.5R to solve for R.
L = 1.5R
40 = 1.5R
To isolate R, we divide both sides of the equation by 1.5:
40/1.5 = R
26.67 = R
Therefore, the radius for a curve with a 40 mile per hour speed limit should be approximately 26.67 feet.
To find the speed limit for a curve with a given radius, you can use the formula L = 1.5R, where L represents the speed limit in miles per hour and R represents the radius of the curve in feet.
Let's solve the given questions step by step:
(a) To find the speed limit for a curve with a radius of 400 feet, substitute R = 400 into the formula:
L = 1.5R
L = 1.5(400)
L = 600
The speed limit for a curve with a radius of 400 feet is 600 miles per hour.
(b) If the radius of a curve doubles, we need to determine the effect on the speed limit. Let's consider a new radius, 2R instead of R:
L = 1.5(2R)
L = 3R
From this, we can see that if the radius doubles, the speed limit will also double. This means that the speed limit is directly proportional to the radius of the curve.
(c) To determine the radius of a curve with a desired speed limit of 40 miles per hour, we can rearrange the formula:
L = 1.5R
Let's substitute the given speed limit and solve for R:
40 = 1.5R
R = 40 / 1.5
R = 26.67 (approx.)
Therefore, the radius of the curve should be approximately 26.67 feet to have a speed limit of 40 miles per hour.