How would I find and interpret the slope of this? (Math Problem)
The Rio Grande has an elevation of about 1150 meters above sea level in El Paso. The length of the river from that point to Brownsville where it enters the sea is about 2400 km. Find and interpret the slope of the river.
Let the elevation represent the y-axis,
Then we have the point (0, 1150) is on one end of the river.
Let the length of the river represent the x -axis
==> the point (2400, 0) in on the other end of the river.
Now the slope of the river (m) is:
m =(y2-y1)/(x2-x1) = (0-1150)/(2400-0)
= -1150/2400 = -0.48 (approx.)
We can take the elivation of the place Rio grande a point R .
We can take the sea level El Paso as E.
We have to presume RP is the river which has a slope.
Therefore the slope of the river could be calculated by completing the triangle in the vertical plane through RE, in which the vertcal line through R and the horizontal line through E meet at G .
Now EGR is right angled triangle with right angle at G.
Threfore the slope (or average) m of the river is given by:
m = GR/EG.
GR = elevation = 1150m
GE = The earth surface distance 2400km = 2400000 meters.
m = GR/sqrt(ER^2-GR^2)
m = 1150/sqrt(2400000^2-1150^2) = 0.0004792 approximately.