Question

multiple choice question
find the magnitude of the sum of a 25.0 n force and a 34.0 n force, given that the angle between the two vectors when aligned tip - to - tail is 125°
1806 n
2.76×10²n
57.5 n
28.4 n

Explanation:

Step1: Use the law of cosines

The formula for the magnitude of the sum of two vectors \(\vec{A}\) and \(\vec{B}\) with an angle \(\theta\) between them is \(R=\sqrt{A^{2}+B^{2}+2AB\cos\theta}\). Here \(A = 25.0\space N\), \(B=34.0\space N\), and \(\theta = 125^{\circ}\), \(\cos(125^{\circ})=\cos(180 - 55)^{\circ}=-\cos(55^{\circ})\approx - 0.5736\).

Step2: Substitute values into the formula

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$$

Answer:

D. \(28.4\space N\)