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Chapter 3: Problem 61

You are walking on a moving walkway in an airport. The length of the walkway is \(59.1 \mathrm{~m}\). If your velocity relative to the walkway is \(2.35 \mathrm{~m} / \mathrm{s}\) and the walkway moves with a velocity of \(1.77 \mathrm{~m} / \mathrm{s}\), how long will it take you to reach the other end of the walkway?

Short Answer

Expert verified
Answer: Approximately 14.3 seconds.

Step by step solution

01

Identify the given information

We are given the following information: - The length of the walkway is \(59.1\,\mathrm{m}\). - The person's velocity relative to the walkway is \(2.35\,\mathrm{m/s}\). - The walkway's velocity is \(1.77\,\mathrm{m/s}\).
02

Calculate the overall velocity

The overall velocity is the sum of the person's velocity relative to the walkway and the walkway's velocity. Therefore, we can denote the overall velocity, \(v\), as follows: \(v = 2.35\,\mathrm{m/s} + 1.77\,\mathrm{m/s}\) Now we can calculate the overall velocity: \(v = 4.12\,\mathrm{m/s}\)
03

Determine the time

To find the time it takes to reach the other end of the walkway, we will use the formula for distance, which is: \(t = \frac{d}{v}\) Here, \(t\) is the time, \(d\) is the distance (the length of the walkway), and \(v\) is the overall velocity. Plugging in the given values, we have: \(t = \frac{59.1\,\mathrm{m}}{4.12\,\mathrm{m/s}}\) Now we can calculate the time: \(t \approx 14.3\,\mathrm{s}\)
04

State the answer

It will take approximately \(14.3\) seconds for the person to reach the other end of the moving walkway.

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