Question

review the graph. two forces of 25 pounds and 20 pounds act on a body with an angle of 25 degrees between them. what is the magnitude of the resultant force? 13.23 pounds 38.78 pounds 43.95 pounds 53.23 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 \( R=\sqrt{F_1^{2}+F_2^{2}+2F_1F_2\cos(180 - \theta)}\) (using the parallelogram law and law of cosines). Here \( F_1 = 25\), \( F_2=20\), and \( \theta = 25^{\circ}\), so \( R=\sqrt{25^{2}+20^{2}+2\times25\times20\times\cos(155^{\circ})}\).

Step2: Calculate each term

• \(25^{2}=625\), \(20^{2} = 400\).
• \(2\times25\times20=1000\), and \(\cos(155^{\circ})\approx - 0.9063\). Then \(1000\times\cos(155^{\circ})\approx-906.3\).

Step3: Compute the value inside the square - root

\(625 + 400-906.3=118.7\).

Step4: Find the square - root

\(R=\sqrt{118.7}\approx38.78\).

Answer:

B. 38.78 pounds