A geologist is studying the erosion rate of a cliff face. If the height of the cliff decreases linearly by 1.5 meters each year, and the current height is 120 meters, how many years will it take for the cliff to erode completely? Assume the erosion rate remains constant.
["Title: How Long Until This Cliff Disappears? Understanding Erosion Rates in Geology", "When studying natural landscapes, one of the key variables geologists track is erosion—the gradual wearing away of rock and earth by wind, water, and other environmental forces. A compelling example involves analyzing the steady erosion of a cliff face, where precise measurements help predict future changes and inform safety and conservation efforts.", "Consider a cliff currently standing at 120 meters tall, with a confirmed linear erosion rate of 1.5 meters per year. This means every year, 1.5 meters of the cliff’s vertical height diminishes. For geologists, modeling such changes is essential to understanding long-term landscape evolution and potential risks, such as rockfalls or habitat loss.", "To determine how many years it will take for the cliff to erode completely, the calculation is straightforward. Since erosion occurs consistently at 1.5 meters annually, divide the current height by the annual erosion rate:", "$$\n\ ext{Years to erode completely} = \frac{\ ext{Current height}}{\ ext{Erosion rate per year}} = \frac{120\ \ ext{meters}}{1.5\ \ ext{meters/year}} = 80\ \ ext{years}\n$$", "This result indicates that, assuming a constant erosion rate of 1.5 meters per year, the cliff will fully disappear in 80 years. While real-world erosion can vary due to weather, rock composition, and human activity, this linear model offers a crucial baseline for geological studies.", "Understanding erosion rates empowers scientists and environmental planners to predict landscape changes, protect nearby infrastructure, and preserve natural heritage for future generations. For the geologist studying this cliff, data like this transforms complex natural processes into actionable knowledge—one measurement at a time.", "In summary, with a height reduction of 1.5 meters per year, a 120-meter cliff will erode completely in just 80 years—called a “complete erosion timeline” that geologists use daily in field studies and risk assessments."]
