Chapter 2: Problem 2
In an experiment, a shearwater (a seabird) was taken from its nest, flown 5150 km away, and released. The bird found its way back to its nest 13.5 days after release. If we place the origin at the nest and extend the +\(x\)-axis to the release point, what was the bird’s average velocity in m/s (a) for the return flight and (b) for the whole episode, from leaving the nest to returning?
Short Answer
Step by step solution
Understand the Given Data
Convert Units for Velocity Calculation
Calculate Average Velocity for Return Flight
Simplify for Part (a)
Understand Displacement for Whole Episode
Calculate Average Velocity for Entire Episode
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Displacement
The key aspect here is that for the entire episode, from the bird leaving the nest and returning, the displacement is zero. This is because displacement considers only the initial and final positions. Since the bird starts and ends at the same place, the net displacement is zero, regardless of the distance travelled.
Importance of Unit Conversion
This conversion is done because the standard unit of velocity in physics is meters per second (m/s). To convert 5150 km to meters, we multiply by 1000 (since 1 km = 1000 m), resulting in 5,150,000 meters.
- 5150 km = 5150 × 1000 = 5,150,000 meters.
Calculating Average Velocity
Using the formula for average velocity:
- \[v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{5,150,000 \, \text{m}}{1,166,400 \, \text{s}}\]
For the entire episode, since the displacement is zero, the average velocity is zero. This illustrates that average velocity depends significantly on the net change in position, not just the distance traveled.
Understanding the Distance-Time Relationship
In this exercise, even though the bird traveled a significant path back to its nest, the time duration (13.5 days converted to seconds) influences the velocity calculation. This highlights an essential understanding:
- Long distance doesn't always translate to high velocity if the duration is extensive.
- Velocity is a vector and can differ considerably from speed, a scalar quantity that considers only distance covered irrespective of direction.