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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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Most popular questions from this chapter

An outfielder throws a baseball with an initial speed of \(32 \mathrm{~m} / \mathrm{s}\) at an angle of \(23^{\circ}\) to the horizontal. The ball leaves his hand from a height of \(1.83 \mathrm{~m}\). How long is the ball in the air before it hits the ground?

Two cannonballs are shot from different cannons at angles \(\theta_{01}=20^{\circ}\) and \(\theta_{02}=30^{\circ}\), respectively. Assuming ideal projectile motion, the ratio of the launching speeds, \(v_{01} / v_{02},\) for which the two cannonballs achieve the same range is a) \(0.742 \mathrm{~m}\) d) \(1.093 \mathrm{~m}\) b) \(0.862 \mathrm{~m}\) e) \(2.222 \mathrm{~m}\) c) \(1.212 \mathrm{~m}\)

Wanting to invite Juliet to his party, Romeo is throwing pebbles at her window with a launch angle of \(37^{\circ}\) from the horizontal. He is standing at the edge of the rose garden \(7.0 \mathrm{~m}\) below her window and \(10.0 \mathrm{~m}\) from the base of the wall. What is the initial speed of the pebbles?

In ideal projectile motion, when the positive \(y\) -axis is chosen to be vertically upward, the \(y\) -component of the velocity of the object during the ascending part of the motion and the \(y\) -component of the velocity during the descending part of the motion are, respectively, a) positive, negative. c) positive, positive. b) negative, positive. d) negative, negative.

A baseball is thrown with a velocity of \(31.1 \mathrm{~m} / \mathrm{s}\) at an angle of \(\theta=33.4^{\circ}\) above horizontal. What is the horizontal component of the ball's velocity at the highest point of the ball's trajectory?
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