/*! 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 118 An airport terminal has a moving... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 118

An airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk; he takes \(150 \mathrm{~s}\) to walk through the corridor. Curly, who simply stands on the moving sidewalk, covers the same distance in \(70 \mathrm{~s}\). Moe boards the sidewalk and walks along it. How long does Moe take to move through the corridor? Assume that Larry and Moe walk at the same speed.

Short Answer

Expert verified
Moe takes approximately 47.73 seconds to move through the corridor.

Step by step solution

01

Determine Larry's Speed

We are given that Larry takes 150 seconds to walk through the corridor without the moving sidewalk. Let \( d \) be the distance of the corridor. Larry's speed \( v_L \) is the distance divided by the time he takes, so we have:\[ v_L = \frac{d}{150} \]
02

Determine the Speed of the Moving Sidewalk

Curly takes 70 seconds to travel the same distance by just standing on the moving sidewalk. Therefore, the speed of the moving sidewalk \( v_S \) is:\[ v_S = \frac{d}{70} \]
03

Find Moe's Combined Speed

Moe walks on the moving sidewalk, so his speed will be the sum of Larry's walking speed and the speed of the sidewalk:\[ v_M = v_L + v_S = \frac{d}{150} + \frac{d}{70} \]
04

Calculate Moe's Time to Cover the Distance

Since Moe's speed \( v_M \) is the combined speed of Larry and the sidewalk, we need Moe's time (\( t_M \)) to cover the distance \( d \). Using the formula \( v = \frac{d}{t} \), we find:\[ t_M = \frac{d}{v_M} = \frac{d}{\left(\frac{d}{150} + \frac{d}{70}\right)} \]
05

Simplify Moe's Time

Simplifying Moe's time:First, find a common denominator for the sum of speeds:\[ v_M = \frac{d}{150} + \frac{d}{70} = \frac{7d}{1050} + \frac{15d}{1050} = \frac{22d}{1050} \]\[ t_M = \frac{d}{\left(\frac{22d}{1050}\right)} = \frac{1050}{22} \approx 47.727 \text{ seconds} \]
06

Conclusion

Moe takes approximately 47.73 seconds to move through the corridor.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Speed Calculation
Speed is one of the foundational concepts you will deal with in relative motion exercises like this one. It can be simply described as how fast something moves. The formula to calculate speed is straightforward:
  • Speed = Distance 梅 Time

The idea is to determine how long it takes to cover a specific distance. In the exercise, Larry's speed is calculated using this fundamental formula. He takes 150 seconds to walk through a corridor of distance \(d\). Thus, Larry's speed \(v_L\) is \( \frac{d}{150} \). This concept helps us understand the role speed plays in comparing different modes of travel across the same distance.
Time and Distance
Time and distance are intricately linked in motion problems. Understanding their relationship helps you compare how long it takes different people or objects to cover the same distance. In our example, the distance \(d\) remains constant, whether someone is walking or standing on the moving sidewalk. The time taken varies based on the speed. Larry takes 150 seconds by walking, whereas Curly takes 70 seconds simply standing, using the moving walkway's speed.
By keeping distance constant, it's easier to compare their respective speeds and time taken. This helps in finding out how the addition of two speeds (as seen with Moe) affects the time it takes to traverse the corridor. Moe benefits from both his walking speed and the speed of the moving sidewalk, leading us to the last important concept: velocity addition.
Velocity Addition
Velocity addition is essential in problems involving multiple speeds or motions. When you combine two velocities, like a person walking on a moving sidewalk, you add the velocities together because they are in the same direction. This total speed then gives you a new perspective on the time taken to travel a distance.In our exercise, Moe's combined speed \(v_M\) is the sum of Larry's walking speed \(v_L\) and the speed of the sidewalk \(v_S\):
  • \( v_M = v_L + v_S \)

This forms the basis for calculating Moe's actual travel time in the corridor. Using velocity addition simplifies the process of determining the new speed with which he moves, demonstrating how these principles help solve real-world relative motion problems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An electron having an initial horizontal velocity of magnitude \(1.00 \times 10^{9} \mathrm{~cm} / \mathrm{s}\) travels into the region between two horizontal metal plates that are electrically charged. In that region, the electron travels a horizontal distance of \(2.00 \mathrm{~cm}\) and has a constant downward acceleration of magnitude \(1.00 \times 10^{17} \mathrm{~cm} / \mathrm{s}^{2}\) due to the charged plates. Find (a) the time the electron takes to travel the \(2.00 \mathrm{~cm},(\mathrm{~b})\) the vertical distance it travels during that time, and the magnitudes of its (c) horizontal and (d) vertical velocity components as it emerges from the region.

A frightened rabbit moving at \(6.00 \mathrm{~m} / \mathrm{s}\) due east runs onto a large area of level ice of negligible friction. As the rabbit slides across the ice, the force of the wind causes it to have a constant acceleration of \(1.40 \mathrm{~m} / \mathrm{s}^{2}\), due north. Choose a coordinate system with the origin at the rabbit's initial position on the ice and the positive \(x\) axis directed toward the east. In unit-vector notation, what are the rabbit's (a) velocity and (b) position when it has slid for \(3.00 \mathrm{~s}\) ?

A particle moves along a circular path over a horizontal \(x y\) coordinate system, at constant speed. At time \(t_{1}=4.00 \mathrm{~s}\), it is at point \((5.00 \mathrm{~m}, 6.00 \mathrm{~m})\) with velocity \((3.00 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{j}}\) and acceleration in the positive \(x\) direction. At time \(t_{2}=10.0 \mathrm{~s}\), it has velocity \((-3.00 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{i}}\) and acceleration in the positive \(y\) direction. What are the (a) \(x\) and (b) \(y\) coordinates of the center of the circular path if \(t_{2}-t_{1}\) is less than one period?

A cat rides a merry-go-round turning with uniform circular motion. At time \(t_{1}=2.00 \mathrm{~s}\), the cat's velocity is \(\vec{v}_{1}=\) \((3.00 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{i}}+(4.00 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{j}}\), measured on a horizontal \(x y\) coordinate system. At \(t_{2}=5.00 \mathrm{~s}\), the cat's velocity is \(\vec{v}_{2}=(-3.00 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{i}}+\) \((-4.00 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{j}}\). What are (a) the magnitude of the cat's centripetal acceleration and (b) the cat's average acceleration during the time interval \(t_{2}-t_{1}\), which is less than one period?

A train at a constant \(60.0 \mathrm{~km} / \mathrm{h}\) moves east for \(40.0 \mathrm{~min}\), then in a direction \(50.0^{\circ}\) east of due north for \(20.0 \mathrm{~min}\), and then west for \(50.0 \mathrm{~min}\). What are the (a) magnitude and (b) angle of its average velocity during this trip?
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Force

Read Explanation

Electric Charge Field and Potential

Read Explanation

Classical Mechanics

Read Explanation

Magnetism

Read Explanation

Quantum Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.