Antonio enjoys mountain biking. He has found that the maximum gradient which he can
cycle up is 0.3 and the maximum gradient he can safely descend is 0.5. Antonio’s map has
a scale of 2 cm to 1 km with contours every 25 m. What is the minimum distance between
the contours (lines on a map showing the height of land) on his map that allows him to go
Answers
Answer:
A distance x on the map (in cm) translates into an actual horizontal distance (in m) of
x%2A%281km%2F%222+cm%22%29%2A%281000m%2F%221+km%22%29=500x
Antonio can go up from one contour line on the map to the next
over a path with a distance x if
25%2F500x%3C=0.3 --> x%3E=25%2F%28500%2A0.3%29cm --> highlight%28x%3E=0.17cm%29 (1.7mm).
(I rounded that result because I assume Antonio cannot see the difference between 1.7mm and 1.66666...mm).
if Antonio wants to follow an uphill path with a distance between contour lines of 0.2cm (2mm) he will be going up 25m, over a horizontal distance of
0.2cm%2A%281km%2F%222+cm%22%29%2A%281000m%2F%221+km%22%29=100m .
That corresponds to a gradient of 25m%2F100m=0.25 ,
Antonio can cycle up that path.
When going downhill the x (in cm) should satisfy
25%2F500x%3C=0.5 --> x%3E=25%2F%28500%2A0.5%29cm --> highlight%28x%3E=0.10cm%29 (1.0mm).
Step-by-step explanation:
Answer:
Hope it helps ^_^
Step-by-step explanation:
