A roller coaster moves 85 m horizontally then travels 45 m at an angle of 30.0 degrees above the horizontal. What is its displacement from its starting point. Use graphical techniques?

Answer 1

On a sheet of graph paper turned sideways, place a point 'A' near the left edge and about midway between top and bottom. From that point, draw a line to the right 85 units. (You may need to consider each 1/4" square to be 5 units and thus draw the line a distance of 85/5 = 17 squares.) Mark the end of that line as point 'B'. From 'B', draw a line toward the right but upward at a 30-degree angle. (Use a protractor to make the angle, or draw a line that rises 1 unit for every 2 units along the line.) Measure 45 units along that line (or 45/5 = 9 units) and mark that point as 'C'. Now measure the distance from point 'A' to point 'C' in the same scale you used for the other distances; that is your answer, in meters. (If one 1/4" square is representing 5 units, or meters, then multiply by 5 the number of quarter-inches you measure from 'A' to 'C'.) Your answer should be a bit less than 130 m (the sum of 85 m + 45 m).