Question

A sand dune can travel up to \(30 \mathrm{~m}\) per year. How far does the sand dune move per day?

Short answer

The sand dune moves approximately 0.0822 meters per day.

Step-by-step solution

Understanding the Problem

We need to find out how far a sand dune moves in one day, given that it travels up to \(30\) meters per year. We'll start by converting the distance traveled per year into a daily distance.

Conversion of Time Units

First, convert the unit of time from years to days. There are approximately \(365\) days in a year. Thus, to find how much the dune moves per day, we need to divide the yearly movement by \(365\).

Calculation

The distance moved per year by the sand dune is \(30\) meters. To find the daily distance moved, calculate \(\frac{30}{365}\approx 0.0822\) meters per day.

Conclusion

We conclude that the sand dune moves approximately \(0.0822\) meters per day when rounded to four decimal places.

Key concepts

Conversion of Time Units

When solving problems that involve time, it's essential to understand how to convert units appropriately. In this context, we're taking annual travel distance, which is how far the sand dune moves in a year, and converting it to a daily travel distance. Knowing that there are approximately 365 days in one year helps to simplify this process.

Here’s how you can perform the conversion:

• Identify the total time frame you're dealing with. Here, it's one year.
• Establish the smaller time unit you want to convert to—in this case, days.
• Use the given conversion factor, which is 365 days for one year, to divide the annual distance.

By dividing the yearly movement (30 meters) by 365 days, you convert the measure from per year to per day, allowing you to manage or interpret daily changes more effectively.

Distance Calculation

Calculating distances over various time frames is a fundamental part of understanding movement. In our exercise, we aim to calculate how far a sand dune travels each day, starting with its annual movement. The method is straightforward:

First, we know how far the dune moves in a year—30 meters. We take this yearly distance and divide it by the number of days in a year, 365 in this case, to find the daily distance. This is mathematically represented as: \[\text{Daily distance} = \frac{\text{Annual distance}}{\text{Number of days in a year}}\]For our specific case, this calculation is: \[\text{Daily distance} = \frac{30 \text{ meters}}{365 \text{ days}} \approx 0.0822 \text{ meters per day}\]Through this calculation, we smoothly transition from a longer-term measurement to a short-term daily understanding of movement.

Annual Travel Distance

Understanding the annual travel distance is crucial when analyzing the movement patterns of objects like sand dunes. Annual travel distance refers to how far something moves throughout the course of a year. For sand dunes, this needs to be understood as a maximum potential movement since their speed can vary due to wind or other environmental factors.

In the example we've been discussing, the sand dune can move up to 30 meters in a year. This gives a measure of how much the dune is capable of drifting due to natural forces, providing valuable insight into landscape changes over time. It's important to consider the entire time span when assessing movement to get an accurate picture of environmental dynamics. This annual measure becomes the baseline for converting larger movements into shorter, more manageable intervals, like daily movement.

Daily Movement

Translating natural movements, like that of a sand dune, into daily figures helps simplify and track these changes effectively. Daily movement gives us a consistent way to measure, compare, and potentially predict movement over time. To compute the daily movement, having an annual figure makes things simple.

As we calculated before, the daily distance moved by the sand dune is approximately 0.0822 meters. This small daily measure can add up over time to the annual shift of 30 meters. Daily movement calculations give geologists and other environmental scientists a clearer understanding of how landscapes are transformed progressively rather than all at once. Remember, regular monitoring of small daily changes can lead to insightful observations about larger environmental trends.