Slope

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#7 - Slope

I stepped out of the car, stretching my legs from the seemingly endless car ride. Once my family and I finished grabbing our things, we headed towards the trailhead that we had driven so long for. I couldn’t help but notice the overwhelming amount of people as we approached the crowded trailhead. Did they not think about the looming volcano they were in front of? I suddenly remembered learning about Mt. St. Helens and its devastating eruption in elementary school, and even more so how it frightened me. I tried to brush away my thoughts, knowing it would only distract me from enjoying the scenery. My family began our hike and within a few minutes, we had reached a viewpoint. The viewpoint revealed the great and historical volcano from a safe distance away. I quickly noticed how flat it appeared compared to other mountains I’ve seen. As we walked to the next viewpoint, I continued to ponder about its slope and how it could’ve changed after the eruption.

The slope is found by dividing the change in y over the change in x. We can represent this with the formula as follows:

For instance, if you wanted to find the slope of a steep road, you first would choose two points on the road: 1st point: (x₁ , y₁), 2nd point: (x₂ , x₂). Using the formula for slope above, you can find the change in y divided by the change in x, resulting in the slope.

By using this formula, we can see how the average slope of Mt. St. Helens’ cone has changed before and after the eruption in 1980. First, we need to identify two points to put into the slope formula. These two points can be anywhere on the slope we want to find. The first point (10.56, 9.677) represents the summit of Mt. St. Helens prior to the eruption. We determined the summit’s coordinates by utilizing half of the cone’s width for our x-coordinate and the elevation of the mountain for our y-coordinate. The second point (0, 4.4) represents the bottom of the mountain’s cone before the eruption¹.

Now that we have two points, we can put them into our slope formula.

Again, we need to identify two points to put into the slope formula. The first point still represents the summit of Mt. St. Helens, but it is now (15.84, 8.364). The second point (0, 4.4) continues to represent the bottom of the mountain slope after the eruption.

Now that we have two points, we can put them into our slope formula.

Now that we have identified our slopes, we can compare them using a ratio. The ratio of the slope before and after the eruption is 2:1.

Slope is a useful math concept as it is found everywhere naturally occurring, from mountains to the ocean floor. However, it is important to mention that there were some limitations in my data. For instance, for simple reference and understanding, we assumed the peak of Mt. St. Helens was always at the center of the mountain. This isn’t always true, which will affect the accuracy of our data and math. But how does this affect us? Well, our calculations of slope show how natural disasters can alter our environment. We can then prepare for similar disasters in advance by keeping areas closer to volcanoes cleared or evacuated quickly.

References

¹Mount St. Helens. (n.d.). McGill School Of Computer Science. Retrieved February 22, 2022, from https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/m/Mount_St._Helens.htm