Question

Slope Gravity is a very powerful erosional force. This means the steeper a slope is, the more soil will move. A person can calculate how steep a slope is by using the height (rise) divided by the length (run). This answer is then multiplied by 100 to get percent slope. If you had a slope \(15 \mathrm{~m}\) high and \(50 \mathrm{~m}\) long, what would be the percent slope?

Short answer

The percent slope is 30%.

Step-by-step solution

Identify Given Values

First, identify the values given in the problem. We have the height or 'rise' of the slope as \(15\, \text{m}\) and the length or 'run' of the slope as \(50\, \text{m}\).

Calculate the Slope Ratio

Calculate the slope ratio by dividing the rise by the run: \( \frac{15}{50} \).

Simplify the Slope Ratio

Simplify the fraction \( \frac{15}{50} \) by dividing both numerator and denominator by 5. This gives \( \frac{3}{10} \).

Convert to Percent Slope

To convert the slope ratio to a percent, multiply by 100. Thus, \( \frac{3}{10} \times 100 = 30\% \).

Conclusion

Thus, the percent slope of the hill is \(30\%\).

Key concepts

Erosional Force

Erosional force is a natural process where materials such as soil, rocks, and other particles are worn away and moved from one place to another. This process can be driven by factors like gravity, water, wind, and ice. In the context of slopes, gravity plays a significant role. A steep slope will often have a stronger erosional force, as gravity pulls more particles downward faster.
Understanding erosional force is crucial because it affects landscapes dramatically. It can lead to landslides, shape valleys, and even alter ecosystems. Key factors that influence erosional force include:

• The steepness of the slope - the steeper it is, the stronger the force.
• The composition of the surface materials - loose soil erodes faster than bedrock.
• Weather and climate conditions - heavy rainfall can accelerate erosion.

By analyzing these factors, geologists can predict erosion patterns and help mitigate the impact on human activities and natural habitats.

Percent Slope

Percent slope is a numerical representation of the steepness or incline of a terrain. It is calculated by dividing the vertical rise by the horizontal run and then converting this ratio into a percentage by multiplying by 100.
For example, in a slope that is 15 meters high and 50 meters long, you start by calculating the rise over run: \( \frac{15}{50} \).
To calculate the percent slope, multiply this result by 100:
\( \frac{15}{50} \times 100 = 30\% \).
Thus, the percent slope is 30%.
Percent slope is an important metric in various fields such as engineering, construction, and environmental science because it informs decisions about land use, construction, and soil management. It helps determine if a slope is stable enough for building or likely to erode, requiring soil reinforcement or other stabilization methods.

Mathematical Solution

Finding solutions to problems involving slope calculation relies on a step-by-step mathematical approach. Beginning with identifying the known values, the height (rise) and length (run), you can determine the slope's steepness ratio.
This exercise follows a sequence:

• Identify given values - in this case, the rise is 15 meters, and the run is 50 meters.
• Calculate the slope ratio by dividing the rise by the run: \( \frac{15}{50} \)
• Simplify the fraction if possible. Here, \( \frac{15}{50} \) simplifies to \( \frac{3}{10} \).
• Convert the slope ratio to a percent by multiplying by 100: \( \frac{3}{10} \times 100 = 30\% \).

Each step moves you closer to understanding the landscape's steepness.
This process can be applied to any slope measurement problem, making it a valuable tool in everyday situations or professional contexts.

Geomorphology

Geomorphology is the scientific study of the Earth’s surface, focusing on its formation, evolution, and the processes that change its shape and structure over time. This field combines aspects of geology, geography, and environmental science to understand how various forces like erosional forces, weathering, and human activity shape the landscapes around us.
Understanding geomorphology is essential for planning and development, hazard assessment, and conservation. It helps answer questions such as:

• How do landscapes change over time?
• What factors are responsible for these changes?
• How can we predict future landscape transformations?

Researchers study landforms, analyze slope gradients, and assess soil stability to provide insights into environmental and ecological management.
Geomorphology helps explain why percent slope is so critical. Changes in slope affect erosion rates, which can alter the geomorphology of an area. Thus, understanding the interplay between erosion, slope, and geomorphic processes helps in managing land sustainably and mitigating natural hazards.