Math Problem Statement

Three players on a reality TV show are given three displacements: A: 72.4 m, 32.0° east of north; B: 57.3 m, 36.0° south of west; C: 17.8 m due south. What does the winner calculate to find the final location? Compute the resultant displacement and direction using a scale diagram and component method.

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Displacement
Trigonometry
Component Method

Formulas

Vector Components: Ax = A * cos(θ), Ay = A * sin(θ)
Resultant Displacement: R = sqrt(Rx^2 + Ry^2)
Direction: θ = arctan(Ry / Rx)

Theorems

Pythagorean Theorem
Trigonometric Identities

Suitable Grade Level

High School (Grades 10-12)

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