# "Terrestrial distance" question

1. Mar 3, 2015

### RJLiberator

1. The problem statement, all variables and given/known data
(Reading topography). The figure above shows the topographical contour map of the Mount Saint Helens in Oregon State. Numbers on the contours indicate elevation in meters above sea level.

(c) The horizontal distance on the map between points F and G is 50 meters. Assuming that the slope of the mounting between these two points remains constant calculate the actual terrestrial distance between them.
(d) Find the slope itself (you may use a calculator to answer these questions).

2. Relevant equations

3. The attempt at a solution
To me, this is a poorly written question. Perhaps someone here can help me understand?

So, we see on the image here:

That the distance between F and G is 50 meters in the horizontal direction.
We also can conclude that there is some height difference of 250 meters.
My initial plan was simply to make a right triangle with height = 250 m and horizontal distance = 50 and thus the hypotenuse (slope) would be sqrt(250^2+50^2).

However, in part D it tells us to 'find the slope' so clearly I am not doing something right.

Perhaps someone can help me understand what the question is asking? What is terrestrial distance? Is it simply 50+250=300m?

2. Mar 3, 2015

### Staff: Mentor

Mt. St. Helens is in Washington state...

3. Mar 3, 2015

### RJLiberator

The initial question was copy-pasted directly from the worksheet, perhaps there is a mistake with their reference, however, am I proceeding correctly to find the answer to this problem?

4. Mar 3, 2015

### Staff: Mentor

The 50 m. is the horizontal distance and the vertical distance between the two contour lines is 250 m., so the distance up the slope is as you said, $\sqrt{50^2 + 250^2}$.
To calculate the slope, use $\frac{\text{rise}}{\text{run}}$

5. Mar 3, 2015

### RJLiberator

So the terrestrial distance is sqrt(50^2+250^2).
This makes clear sense.

Rise is 250, run is 50, so the slope is then 5. Ah... easy enough.

For some reason, when conceptualizing the question I considered them the same thing. Thank you for the clarification.

I'll let them know about the mixup with the mountain. :p

6. Mar 3, 2015

### Staff: Mentor

Not "perhaps" -- they are flat wrong. From the top of St. Helens you can look south and see Oregon, but the mountain is definitely not in Oregon.

7. Mar 4, 2015

### HallsofIvy

Staff Emeritus
I used to live in a suburb of Portland, Ore. I could look north from my back yard and see Mt St Helens- but it was definitely across the Columbia River and definitely in Washington. I could look east and see Mt Hood. Perhaps that was the confusion.

8. Mar 4, 2015

### Staff: Mentor

The contour map in post #1 is definitely that of post-eruption Mt. St. Helens. Before the eruption, the contours were roughly circular. Now they are U-shaped, open to the north, the direction of the lateral blast that hollowed out the once-symmetric peak.

9. Mar 4, 2015

### HallsofIvy

Staff Emeritus
Right. I still want to cry when I think what a beautiful mountain St. Helen's was. It look like a scoop of ice-cream! Of course, that beautiful round summit was because of the volcanic pressure inside.

10. Mar 4, 2015

### Staff: Mentor

Here's a picture I took in 1971. It was called "America's Mt. Fuji" for its similarity to the Japanese peak. A few friends and I climbed it in '75. Another guy and I made a winter attempt in early Jan, '79 (a little over a year before it exploded). We weren't able to make the summit on that trip, due to whiteout conditions.

To the OP -- sorry for dragging this thread off-topic...

11. Mar 4, 2015

### HallsofIvy

Staff Emeritus
Thanks, Mark, I'm saving that picture on my computer. Is that "Spirit Lake" in the fore ground?

12. Mar 4, 2015

### Staff: Mentor

No, I'm pretty sure that's the Columbia River. It's a long time back but I think I took the picture right after I had crossed over into Washington.