a high way curve is to be laid out on a circle. what radius should be used if a trailer truck is to change direction by 28 degrees in a distance of 112 meters?
since s = rθ,
r = s/θ = 112/(28 * π/180) = 229m
To find the radius of the curve needed for the trailer truck to change direction by 28 degrees in a distance of 112 meters, we can use the formula for the arc length of a circle.
The formula for the arc length is:
Arc Length = (θ/360) × 2πr
Where:
- Arc Length is the distance traveled along the circumference of the circle
- θ is the central angle of the curve in degrees
- r is the radius of the circle
We know that the truck changes direction by 28 degrees in a distance of 112 meters. Plugging these values into the formula, we have:
112 = (28/360) × 2πr
Simplifying the equation:
112 = (7/90) × 2πr
To isolate the radius, divide both sides of the equation by (7/90) × 2π:
112 / [(7/90) × 2π] = r
Now, we can calculate the value of r using this equation.