Task 3. Now that you know the relationship between a curved road…
QuestionAnswered step-by-stepTask 3. Now that you know the relationship between a curved road…Task 3. Now that you know the relationship between a curved road radius and the speed limit for safe travel, you are tasked with determining if an existing curved road is safe to travel under the current speed limit set. You will use data provided by surveyors that report to you three locations along the curved road. You need to determine the radius of the curved road from the three locations given. Then use it to determine if the current speed limit is acceptable for safe travel. A Geomatics graduate surveys the curve and reports the following three locations on the midline of the road in the curve. Surveyors measure distances from a set location, called STATIONS. A station is chosen such that all possible designs will stay in Quadrant I. The current speed limit on the curved road is 65 MPH. Assume 4% superelevation for all the following tasks. To reduce these numbers to make them more manageable, set a new STATION at 9000 feet North and 3000 feet East from the original STATION. Also, change the Northern distances to be the second number in your coordinate location and the Eastern distances to be the first number in your coordinate location. A) Complete the table below for the adjusted locations of points A, B, and C using the STATION at 9000 feet North and 3000 feet as the location (0,0). (Remember: Change the adjusted Northern distance to the y-coordinate and change the adjusted Eastern distance to the x-coordinate.) Point Labels North from Station (ft) East from Station (ft) A 9249 3701 B 9196 3824 C 9161 3958 Point Labels Horizontal x-axis Vertical y-axis A 701 249 B 824 196 C 958 161 Road Design Engineers use circles to model curves in roads and they use the term HORIZONTAL CURVES. Below is a diagram of a horizontal curve and a common formula used to find the radius of the horizontal curve. Image transcription textHORIZONTAL CIRCULAR CURVES Pi D = Degree of curve, are definition L – Length of curve from P.C. to P.T. EGib = Length of sub-chord ( = Length of are for sub-chord d = Central angle for sub-chord C PC. LC 5,729.58 RAC T – R tan (1/2) R 2 sin (a + b) L-RI 2b 28 “180 (100) LC-2R sin (12) c – 2R sin (d/2) NOT T… Show more B) Determine the distances between each of the points A, B, and C. Segment Length AB BC AC C) Determine the interior angles of the triangle ABC. Angle Degrees a b c D) Determine the radius of the curved road. E) Is the current speed limit set on this curve safe to travel? Why or why not? F) If not, adjust the location of point B, so that it is safe to travel at 65 MPH. Give the location of the new point B. G) Construction costs for a two lane road is between $3 million per mile and $5 million per mile in urban areas. Assuming a cost of $4 million per mile, determine a projected cost of constructing the new designed curve. MathTrigonometryMAT 121Share Question
