While Driving down a mountain, top finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. find the slope of his decent to the nearest hundredth.
I am not sure where to start on this equation. I know that m = y2-y1 over x2-x1, but I am not sure how to set this one up. Any suggestions or clues?
Thank you!
Russell
You must have heard the alternate way to define slope as rise/run
the rise is 1800 ft, for a run of 3.25 miles.
slope usually has not units (they cancelled out in the calculation), so you must have the same units.
there are 5280 feet in 1 mile, so change the 3.25 miles into feet
then form the fraction,
I had it reduce to 15/143
if you want to set it up your way, you would have two points (0,0) and (17160,1800) now do the y2... bit stuff
To find the slope of the descent, you can use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
In this case, let's consider the points (0, 0) as the starting point and (17160 ft, 1800 ft) as the final point.
The change in elevation (rise) is 1800 ft, and the horizontal distance (run) is 17160 ft.
To find the slope, plug these values into the formula:
slope (m) = (1800 ft - 0 ft) / (17160 ft - 0 ft)
Simplifying the equation:
slope (m) = 1800 ft / 17160 ft
To compare the units, convert the 3.25 miles into feet:
3.25 miles * 5280 ft/mile = 17160 ft
Now, substitute the values again:
slope (m) = 1800 ft / 17160 ft
Calculating this fraction gives you:
slope (m) = 0.1048951048951049
When rounded to the nearest hundredth, the slope of the descent is approximately 0.10.