Question

review the diagram. two forces with magnitudes 300 pounds and 450 pounds, with an angle of 60° between them, act upon an object. what is the approximate magnitude of the resultant force? 409.81 pounds 600.00 pounds 653.91 pounds 859.81 pounds

Explanation:

Step1: Apply the law of cosines

The formula for the magnitude \( R \) of the resultant of two vectors \( F_1\) and \( F_2\) with an included angle \(\theta\) is \( R=\sqrt{F_1^{2}+F_2^{2}+2F_1F_2\cos\theta}\). Here, \(F_1 = 300\), \(F_2=450\), and \(\theta = 60^{\circ}\), \(\cos60^{\circ}=\frac{1}{2}\).

Step2: Substitute values into the formula

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Step3: Calculate the square - root

\(\sqrt{427500}\approx653.91\) (using a calculator).

Answer:

C. 653.91 pounds