Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 03: Motion in Two or Three Dimensions

Problem 31b

Chapter 3, Problem 31b

A 'moving sidewalk' in an airport terminal moves at 1.0 m/s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take her to reach the opposite end if she walks In the opposite direction?

Verified step by step guidance

First, understand the scenario: The woman is walking in the opposite direction to the moving sidewalk. This means her walking speed relative to the ground will be the difference between her walking speed and the sidewalk's speed.

Calculate her effective speed relative to the ground. Since she is walking opposite to the direction of the sidewalk, subtract the sidewalk's speed from her walking speed: $ v_{effective} = v_{walk} - v_{sidewalk} $.

Substitute the given values into the equation: $ v_{effective} = 1.5 \text{ m/s} - 1.0 \text{ m/s} $.

Now, use the formula for time, $ t = \frac{d}{v} $, where $ d $ is the distance and $ v $ is the effective speed. The distance $ d $ is given as 35.0 m.

Substitute the values into the time formula: $ t = \frac{35.0 \text{ m}}{v_{effective}} $. This will give you the time it takes for her to reach the opposite end.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Relative Velocity

Relative velocity is the velocity of an object as observed from a particular frame of reference. In this problem, the woman's walking speed relative to the moving sidewalk is 1.5 m/s, and the sidewalk itself moves at 1.0 m/s. Understanding how these velocities combine or oppose each other is crucial for determining her actual speed relative to the ground.

Vector Addition

Vector addition involves combining vectors to determine a resultant vector. Here, the woman's walking velocity and the sidewalk's velocity are vectors that need to be added or subtracted depending on the direction of her walk. If she walks in the opposite direction, her effective velocity relative to the ground is the difference between her walking speed and the sidewalk's speed.

Time Calculation

Time calculation involves determining the duration it takes to cover a certain distance at a given speed. Once the effective velocity is found, the time taken to traverse the 35.0 m length of the sidewalk can be calculated using the formula: time = distance/speed. This concept is essential for solving the problem and finding the time required for the woman to reach the opposite end.

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Textbook Question

A 'moving sidewalk' in an airport terminal moves at 1.0 m/s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take her to reach the opposite end if she walks in the same direction the sidewalk is moving?

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