Math Problem Statement

A force of magnitude FN acts in a horizontal plane and has components 27.5 N and -24 N in the x-direction and the y-direction respectively. The force acts at an angle of a below the x-axis.

(i) Find the values of F and a.

A second force, of magnitude 87.6 N, acts in the same plane at 90° anticlockwise from the force of magnitude FN. The resultant of the two forces has magnitude RN and makes an angle of 0° with the positive x-axis.

(ii) Find the values of R and 0.

Solution

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Math Problem Analysis

Mathematical Concepts

Vectors
Trigonometry
Resultant Forces

Formulas

Pythagorean theorem
Vector addition
Angle calculations using trigonometry

Theorems

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Suitable Grade Level

High School