/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 In an experiment, a shearwater (... [FREE SOLUTION] | 91Ó°ÊÓ

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In an experiment, a shearwater (a seabird) was taken from its nest, flown 5150 \(\mathrm{km}\) away, and released. The bird found its way back to its nest 13.5 days after release. If we place the origin in the nest and extend the \(+x\) -axis to the release point, what was the bird's average velocity in \(\mathrm{m} / \mathrm{s}(\) a) for the return flight, and (b) for the whole episode, from leaving the nest to returning?

Short Answer

Expert verified
(a) 4.41 m/s; (b) 0 m/s.

Step by step solution

01

Convert Distance to Meters

The distance given is 5150 km. To use the distance in our velocity calculation, we need it in meters. We know that 1 km = 1000 m.Thus, the distance in meters is computed as:\[5150 \times 1000 = 5,150,000\, \text{meters}\]
02

Convert Days to Seconds

The time taken for the bird to return is 13.5 days. We need this in seconds for our velocity calculation. Since there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, the conversion is:\[13.5 \times 24 \times 60 \times 60 = 1,166,400\, \text{seconds}\]
03

Calculate Average Velocity for Return Flight

The average velocity for the return flight is the total displacement divided by the total time. Since the displacement is 5,150,000 meters and the time is 1,166,400 seconds:\[\text{Average velocity} = \frac{5,150,000}{1,166,400} \approx 4.41\, \text{m/s}\]
04

Consider the Whole Episode

For the whole episode, the bird started and ended at the same point. Therefore, the total displacement is 0 meters because the starting and ending points are the same.
05

Calculate Average Velocity for Whole Episode

The average velocity is calculated based on the total displacement over the total time. Since the total displacement is 0 meters, the average velocity for the entire episode is:\[\text{Average velocity} = \frac{0}{1,166,400} = 0\, \text{m/s}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Displacement
Displacement is a core concept in physics that helps us understand movement in relation to a specific point of reference. It's different from distance, as displacement only considers the overall change in position. Displacement measures how far out of place an object is; it’s the object’s overall change in position. For example, if a shearwater flies from its nest and returns to the exact same spot, its total displacement is zero.
In the context of the shearwater exercise, while the bird traveled a long distance of 5150 km, the net displacement for the entire episode is zero because it started and ended at the same place. Displacement is a vector quantity, which means it has both a magnitude and a direction. In this case, the direction does not change because the shearwater returns to its origin. This can be a bit confusing, but it highlights the importance of differentiating between distance and displacement.
Simplifying Conversion of Units
Before we can calculate the average velocity, we need to make sure that all measurements are in compatible units. Often, problems will give information in various units such as kilometers, miles, days, or hours. To calculate velocity, which is typically measured in meters per second (m/s), we must convert all distances to meters and all time measurements to seconds.
  • To convert kilometers to meters, multiply by 1000. For instance, 5150 km becomes 5,150,000 meters.
  • Converting days to seconds requires multiple steps: 1 day is equivalent to 24 hours, 1 hour is 60 minutes, and 1 minute is 60 seconds. So, 13.5 days translates to 1,166,400 seconds.
These conversions might seem like extra work, but they help ensure that the final calculations are done accurately and consistently.
The Basics of Velocity Calculation
Velocity is a measure of how quickly an object changes its position. It's important to note that velocity is different from speed. Speed is scalar and only measures how fast an object is moving, while velocity is a vector and includes direction. Average velocity is calculated by dividing the total displacement by the total time taken.
For our shearwater example, after returning to its starting point, the average velocity during its journey is calculated by dividing the displacement by the time. For the return flight, it covers a displacement of 5,150,000 meters in 1,166,400 seconds, leading to an average velocity of approximately 4.41 m/s. However, for the entire round trip, the displacement is zero, resulting in an average velocity of 0 m/s. This highlights the distinction between displacement and distance covered.
Exploring Shearwater Navigation
Shearwater navigation is a fascinating phenomenon, as these seabirds can find their way back over vast distances. This skill likely relies on a complex combination of innate instincts and environmental cues. When scientists study such feats of navigation, they look at how animals use visual landmarks, the position of the sun and stars, and even the Earth's magnetic field.
In our exercise, the shearwater successfully traversed the distance of 5150 km back to its nest. Understanding how these birds navigate can provide insights into broader topics such as animal migration and orientation in the animal kingdom. It’s an intriguing intersection of biology and physics where understanding environmental navigation offers an exciting lens for interpreting animal behavior. The use of velocity and displacement in this context further enriches our understanding of how effectively these birds move through space over time.

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Most popular questions from this chapter

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