/*! 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 34 Suppose an airline trip of \(100... [FREE SOLUTION] | 91Ó°ÊÓ

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Suppose an airline trip of \(1000 \mathrm{~km}\) takes \(3 \mathrm{~h}\) with about \(30 \mathrm{~min}\) of that spent taxiing, taking off, and landing. Estimate your average speed while airborne.

Short Answer

Expert verified
The average speed while airborne would be \(400 \mathrm{~km/h}\).

Step by step solution

01

Convert Time to Hours

Firstly, convert the taxiing, taking off and landing time from minutes to hours. As we know there are 60 minutes in an hour, so \(30 \mathrm{~min} = \frac{30}{60} = 0.5 \mathrm{~h}\).
02

Calculate Time Airborne

Next, we need to calculate the time the plane was airborne. This would be the total trip time minus taxiing, taking off, and landing time. So, that would be \(3 \mathrm{~h} - 0.5 \mathrm{~h} = 2.5 \mathrm{~h}\).
03

Calculate Average Speed

Finally, calculate the average speed using the formula: speed = distance/time. So, the speed would be \( \frac{1000 \mathrm{~km}}{2.5 \mathrm{~h}} = 400 \mathrm{~km/h}\).

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Key Concepts

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

Distance-Time Relationship
The connection between distance and time is foundational in understanding movement. Largely, kinematics relies on this relationship. In travel scenarios, the distance is the span covered between start and destination, while time refers to the duration taken for this journey.

To delve deeper, think of the path an object, like a plane, travels. Break the total time into parts: the actual flying and other activities, such as taxiing. For the exercise, flying time excludes the half-hour spent on other activities like taking off. This narrows our focus to just the time the plane was airborne.

In general terms, the formula to decipher average speed: \[\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\]
This formula lets you understand how fast an object moves between two points during a specific period. The relationship helps you calculate essential travel information. This experience is crucial to various fields, not just aviation.
Unit Conversion
Unit conversion is an indispensable tool. It lets you manipulate data across various measurement systems. This is especially useful in fields like physics and engineering. Sometimes, you'll find data in differing units and need to convert these to a common standard.

For instance, time was originally in minutes (30 min) in our exercise. Converting this to hours (0.5 h) aligned it with the total trip time, making calculations straightforward. The key point here is recognizing the conversion factor, such as:
  • 1 hour = 60 minutes
Using conversion allows seamless integration of various data formats. It bridges gaps between data, allowing for accurate and error-free calculations.
Kinematics
Kinematics is the branch of physics that examines motion. It cares more about how objects move, not why they move. Here, we focus on the object’s velocity, distance covered, and the parameters affecting its motion.
Understanding kinematics helps you estimate things like a plane’s average speed when airborne. Motion breaks down into several phases; understanding how each contributes to the overall movement helps calculate such parameters efficiently.
Average speed is a critical concept. It blends distance and time to give a bird’s-eye view of how fast an object travels. Kinematics not only examines straightforward motion but also complex flight patterns. When calculating airborne speed, you're observing a simplified kinematics study, tracking how far and how fast the plane travels amidst different phases of flight.

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Most popular questions from this chapter

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