Question

Rubber Ducks A severe storm on January 10, 1992, near the Aleutian Islands, caused a cargo ship to spill 29,000 rubber ducks and other bath toys into the ocean. Ten months later hundreds of rubber ducks began to appear along the shoreline near Sitka, Alaska, roughly \(2600 \mathrm{~km}\) away. What was the approximate average speed, in meters per second, of the ocean current that carried the ducks to shore? (Rubber ducks from the same spill began to appear on the coast of Maine in July 2003.)

Short answer

The approximate average speed of the ocean current was 0.099 m/s.

Step-by-step solution

Convert Distance to Meters

Since the distance given is in kilometers, you first need to convert it to meters. There are 1,000 meters in a kilometer, so multiply the distance by 1,000: \[ 2600 \text{ km} \times 1000 \text{ m/km} = 2,600,000 \text{ m} \]

Calculate Time in Seconds

Next, convert the time from ten months into seconds. - Assume each month has approximately 30.44 days (as the average length of a month):\[ 10 \text{ months} \times 30.44 \text{ days/month} = 304.4 \text{ days} \]- Convert days to hours:\[ 304.4 \text{ days} \times 24 \text{ hours/day} = 7305.6 \text{ hours} \]- Convert hours to minutes:\[ 7305.6 \text{ hours} \times 60 \text{ minutes/hour} = 438336 \text{ minutes} \]- Convert minutes to seconds:\[ 438336 \text{ minutes} \times 60 \text{ seconds/minute} = 26300160 \text{ seconds} \]

Compute Average Speed

The average speed can be calculated by dividing the total distance by the total time taken. Use the formula: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]Substitute the values into the formula:\[ \text{Average Speed} = \frac{2,600,000 \text{ meters}}{26,300,160 \text{ seconds}} \approx 0.099 \text{ meters/second} \]

Key concepts

Unit Conversion

Unit conversion is an essential skill in physics and everyday life to connect different measurement systems. In the exercise, the task was to calculate the average speed of rubber ducks carried by ocean currents. The distance provided was in kilometers, but the speed needed to be found in meters per second. Hence, unit conversion played a crucial role.- **Distance Conversion**: To solve the problem, we first converted the distance from kilometers to meters. Every kilometer is equal to 1,000 meters. Therefore, for our problem: \[ 2600 \text{ km} \times 1000 \text{ m/km} = 2,600,000 \text{ m} \] This simple multiplication gives us the correct units for calculations involving meters per second.- **Time Conversion**: Similarly, we need to change time from months to seconds because speed is in meters per second. Assuming an average month length of 30.44 days, we do the following conversions: \( 10 \text{ months} \times 30.44 \text{ days/month} = 304.4 \text{ days} \) Next, days are converted into hours, hours into minutes, and finally, minutes into seconds. Understanding such conversions helps in forming a complete and consistent measurement system for accurate calculations.

Distance and Time

Understanding the relation between distance and time is vital for calculating speed. Speed is defined as the distance travelled per unit of time. In our exercise, rubber ducks travelled a distance of 2,600 kilometers over a period of ten months. This means we need to understand how distance and time relate to gauge speed appropriately. - **Distance**: The distance for the current problem was the path, approximately 2,600 km, that the ducks travelled due to the ocean currents, which plays a pivotal role in speed calculation. - **Time**: Time taken for this journey was ten months, which, when broken down: - 10 months translate roughly into 304.4 days taking an average month length as 30.44 days. - Further broken down into hours, minutes, and ultimately seconds, time becomes consistent with meters in deriving speed. Without understanding how to accurately measure and convert these measurements, achieving correct results for speed would be impossible. For instance, the conversion from days to seconds ensures consistency with our meter measurement for determining the average speed.

Ocean Currents

Ocean currents are continuous, directed movements of seawater generated by various forces. They play a crucial role in the transport of marine debris like the spilled rubber ducks in our exercise. - **Influence on Movement**: The exercise gives us insight into how ocean currents facilitated the movement of rubber ducks across the ocean from the Aleutian Islands to Sitka, Alaska. These natural water movements are significant in determining the speed and direction of objects floating on the water surface. - **Speed Impact**: Currents can vary in speed and direction, influenced by wind, the Earth's rotation, and water temperature and salinity differences. In the exercise, the average speed was found to be approximately 0.099 meters per second. Understanding ocean currents is not only crucial for calculations like this but also for comprehending the broader impacts on marine navigation, climate, and the movement of oceanic life and debris. Efficient modeling of these currents helps predict where debris or other floating objects might end up, important for environmental studies and clean-up efforts.