ORadicals
Word problem involving radical equations: Basic
Suppose a pendulum is meters long. The time, , in seconds that it
takes to swing back and forth once is given by . If a pendulum is
20.25 meters long, how long does it take to swing back and forth once?
Round your answer to the nearest tenth.
seconds
Explanation CHRISTOPH…

To find the time it takes for a pendulum of length 20.25 meters to swing back and forth, we can plug this value into the given equation: . Plugging in , we get . Calculating the square root, we find . Therefore, seconds. So it takes approximately 9.0 seconds for the pendulum to complete one full swing.

Understanding pendulum motion can be traced back to the 17th century when Galileo discovered that the time of a pendulum’s swing is independent of the mass and angle, solely depending on its length! This concept led to advancements in timekeeping, with pendulum clocks revolutionizing how we measure time, making it possible to achieve unprecedented accuracy. So, every time you check the time, you’re looking at the legacy of pendulum physics!

In practice, when working with radical equations, a common mistake is forgetting to account for both positive and negative solutions of the radical. However, for problems like this, specifically related to time, we only consider the positive solution. Another tip is to ensure your calculator is set appropriately for the calculations, particularly with square roots, as incorrect settings can lead to mistakes in your final answer!