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How long does it take an automobile travel initinllu EE

How long does it take an automobile travel initinllu EE

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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## Problem Description ### Question How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 35.0 km/h when the cars' front bumpers are initially 55 m apart? ### Answer Input Field --------------- _______ s --------------- ### Additional Help Options --- **Need Help?** - **[Read It]** - **[Watch It]** --- ## Explanation for Solution In this problem, we are given: - Speed of the car in the left lane: 60.0 km/h - Speed of the car in the right lane: 35.0 km/h - Initial distance between the front bumpers of the cars: 55 meters To find the time it takes for the car in the left lane to catch up, we need to determine how long it takes to cover the additional 55 meters at the relative speed between the two cars. ### Steps to Solve: 1. **Convert speeds from km/h to m/s:** - Speed of left lane car: \( 60.0 \text{ km/h} = \frac{60.0 \times 1000}{3600} \text{ m/s} = 16.67 \text{ m/s} \) - Speed of right lane car: \(35.0 \text{ km/h} = \frac{35.0 \times 1000}{3600} \text{ m/s} = 9.72 \text{ m/s} \) 2. **Find the relative speed between the two cars:** - Relative speed = \( 16.67 \text{ m/s} - 9.72 \text{ m/s} = 6.95 \text{ m/s} \) 3. **Calculate the time to cover the initial distance with the relative speed:** - Time = Distance / Relative speed = \( \frac{55 \text{ m}}{6.95 \text{ m/s}} ≈ 7.91 \text{ s} \) So, it takes approximately 7.91 seconds for the car in the left lane to overtake the car in the right lane.
Transcribed Image Text:## Problem Description ### Question How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 35.0 km/h when the cars' front bumpers are initially 55 m apart? ### Answer Input Field --------------- _______ s --------------- ### Additional Help Options --- **Need Help?** - **[Read It]** - **[Watch It]** --- ## Explanation for Solution In this problem, we are given: - Speed of the car in the left lane: 60.0 km/h - Speed of the car in the right lane: 35.0 km/h - Initial distance between the front bumpers of the cars: 55 meters To find the time it takes for the car in the left lane to catch up, we need to determine how long it takes to cover the additional 55 meters at the relative speed between the two cars. ### Steps to Solve: 1. **Convert speeds from km/h to m/s:** - Speed of left lane car: \( 60.0 \text{ km/h} = \frac{60.0 \times 1000}{3600} \text{ m/s} = 16.67 \text{ m/s} \) - Speed of right lane car: \(35.0 \text{ km/h} = \frac{35.0 \times 1000}{3600} \text{ m/s} = 9.72 \text{ m/s} \) 2. **Find the relative speed between the two cars:** - Relative speed = \( 16.67 \text{ m/s} - 9.72 \text{ m/s} = 6.95 \text{ m/s} \) 3. **Calculate the time to cover the initial distance with the relative speed:** - Time = Distance / Relative speed = \( \frac{55 \text{ m}}{6.95 \text{ m/s}} ≈ 7.91 \text{ s} \) So, it takes approximately 7.91 seconds for the car in the left lane to overtake the car in the right lane.
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