Answered: An engineer designs a roller coaster so…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section1.8: Some Properties Of Vectors

Problem 1.4QQ

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Question

An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 147 ft at an angle of 33.0° above the horizontal. It then moves 147 ft at an angle of 42.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

magnitude ____ft

direction _____° counterclockwise from the +x-axis

Expert Solution

Step 1: Introduction

From the given information draw a diagram of the roller coaster's motion-

Here,

$stack x subscript 1 with rightwards arrow on top comma space stack x subscript 2 with rightwards arrow on top comma space$ and $stack x subscript 3 with rightwards arrow on top$ are displacement vectors.

According to the given information, the magnitude of these vectors are,

$x subscript 1 equals 162 space ft comma space x subscript 2 equals 147 space ft comma x subscript 3 equals 147 space ft$

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