Question

The Pacific Plate moves north relative to the North American Plate at a rate of \(6 \mathrm{~cm}\) per year. How long will it take Los Angeles (a city on the Pacific Plate) to move northward by \(480 \mathrm{~km}\), the present distance between Los Angeles and San Francisco? (B)

Short answer

It will take \(8,000,000 \mathrm{~years}\) for Los Angeles to move northward by 480 km, the present distance between Los Angeles and San Francisco.

Step-by-step solution

Convert given distance from km to cm

First, we need to convert the distance between Los Angeles and San Francisco from kilometers to centimeters. To do this, we will multiply the given distance (480 km) by the conversion factor, 100,000 (number of centimeters in a kilometer). \[480 \mathrm{~km} \times 100,000 \frac{\mathrm{~cm}}{\mathrm{~km}}\]

Calculate the time

Next, we will calculate the time it takes for Los Angeles to move northward by the converted distance. We do this by dividing the converted distance by the rate of movement (6 cm/year): \[\frac{480 \mathrm{~km} \times 100,000 \frac{\mathrm{~cm}}{\mathrm{~km}}}{6 \frac{\mathrm{~cm}}{\mathrm{~year}}}\]

Simplify the expression

Now, we will simplify the expression: \[\frac{480 \times 100,000 \mathrm{~cm}}{6 \mathrm{~cm} \cdot \mathrm{~year}}\]

Calculate the result

Finally, we will calculate the result: \[\frac{48,000,000 \mathrm{~cm}}{6 \frac{\mathrm{~cm}}{\mathrm{~year}}}\] \[\Rightarrow 8,000,000 \mathrm{~years}\] So, it will take 8,000,000 years for Los Angeles to move northward by 480 km, the present distance between Los Angeles and San Francisco.

Key concepts

Continental Drift

Continental drift is a groundbreaking theory that explains the movement of the Earth's continents over geological time. Introduced by Alfred Wegener in the early 20th century, this theory posits that continents are not static but move across the Earth's surface, driven by the force of plate tectonics.

The idea of continental drift was revolutionary because it suggested that the positions of continents and oceans are not permanent. One of the most compelling pieces of evidence for this theory is the puzzle-like fit of the coastlines of South America and Africa, suggesting they were once joined. Additionally, similar rock formations, fossils, and geological features found on different continents bolster the theory of their past connection.

In our exercise, we discuss the movement of the Pacific Plate relative to the North American Plate, exemplifying the ongoing nature of continental drift. Over millions of years, this movement has resulted in significant changes in the geography of our planet, leading to the world map we know today.

Geological Time Scale

The geological time scale is a system of chronological measurement that relates stratigraphy to time, utilizing the evidence locked in the Earth's rock layers. It divides Earth's history into eons, eras, periods, epochs, and ages, providing a framework for understanding major events in the planet's 4.6 billion-year history.

The scale helps scientists date the events of Earth's past, such as volcanic eruptions, mass extinctions, and the evolution of life forms.

Understanding the geological time scale is crucial when discussing plate movements, as the rate at which the Pacific Plate moves, indicated in the exercise (6 cm/year), is very slow and requires millions of years to cause noticeable changes. Hence, it will take Los Angeles 8,000,000 years to move 480 km northward, based on the current rate of the Pacific Plate's movement. This is an excellent example of the vast scales of time over which geological processes like continental drift operate.

Earth Science Mathematics

Earth science mathematics is the application of mathematical methods and principles to solve problems related to Earth science disciplines, including geology, meteorology, oceanography, and astronomy. In our exercise, we executed a series of calculations to determine the time required for a continental plate to move a specific distance.

The problem required converting units from kilometers to centimeters to match the unit of plate movement rate (cm/year). Then, by dividing the total distance to be traveled by the annual rate of movement, we obtained the time frame in years. These calculations are vital in earth sciences as they allow us to quantify geological processes happening over extensive periods.

Students learning earth science mathematics must be comfortable with unit conversions, working with large numbers, and understanding rates—skills that are essential for accurately interpreting and predicting geological phenomena over time.