Imagine a road on which you lose 250 feet in elevation for every mile driven.

Question

Imagine a road on which you lose 250 feet in elevation for every mile driven.

a). Draw pictures that show a loss of 500 feet in elevation over 2 miles of horizontal distance and 1,000 feet over 4 miles of horizontal distance.

b). Find the slope of the road, using each of the two triangles. Simplify each slope. What do you notice?

c). A 6% grade is the maximum steepness that a truck is able to navigate under company safety guidelines. Can the truck drive on this road?

Answer 1

Answer:

a) Draw a point that has an elevation of zero, and using a scaled ruler to measure draw a point directly underneath it which has an elevation of -500 ft. From the lower point draw a straight line to the right that is 2 miles long (1 mile = 5280 ft, for 2 miles = 10560 ft) and draw using the scale a point at the end of the 2 miles long line. Join the top point at zero elevation to the end point of the line with an inclined line. That inclined line represents a drop of 500' in elevation for a 10560' run ( 2 miles). Do the same for a drop of 1000 ft but this time for 21120 ft ( 4 miles).

b) complete triangles 1 &2 by joining the top and bottom points, and bottom point to the end of lines points to the right. You should have two right angle triangles that are similar but with different scales. Find the slopes of the hypotenuse of the right angle triangles such that the slope of triangle 1 is

S1 = rise/run = 500'/10560' = 0.0473 and the slope S2 of triangle 2 = 1000'/21120'=0.0473

Notice that the slopes are the same such that S1 = S2. From that you can conclude that for the slopes to be equal, the length of the rise and run have to be proportional and therefore the triangles have similar interior angles and the triangles are similar

C) The slope can be expressed in percent such that S% = ( rise/run)*100 = 0.0473(100)= 4.73%. This slope is less than the 6% slope limit for the truck safety rules, and therefore the truck can drive on this road