Math Problem Statement

Emilia's car is stuck in the mud. Deandre and Brigeth come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Deandre and Brigeth get behind the car and push. The truck generates a horizontal force of 318 lb on the car. Deandre and Brigeth are pushing at a slight upward angle and generate a force of 138 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 23.6°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. round to two decimal places

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Addition
Resultant Force
Trigonometry

Formulas

Resultant Force Formula: R = sqrt(F1^2 + F2^2 + 2 * F1 * F2 * cos(θ))
Direction Angle Formula: θ = arctan(Fy/Fx)

Theorems

Law of Cosines

Suitable Grade Level

Grades 10-12