Question

(problem reference m.2) two force vectors are shown in the figure. the magnitudes of the forces are a = 100 n and b = 125 n. what is the x - component of the vector \\( \vec { b } \\)? 52.8 n 57.4 n 81.9 n 125 n 113 n

Explanation:

Step1: Recall the formula for the x - component of a vector

The x - component of a vector \(\vec{B}\) with magnitude \(B\) and angle \(\theta\) (measured from the positive x - axis) is given by \(B_x=B\cos\theta\).

Step2: Identify the values of \(B\) and \(\theta\)

Here, \(B = 125\space N\) and \(\theta=25.0^{\circ}\)

Step3: Calculate \(B_x\)

Substitute the values into the formula: \(B_x = 125\times\cos(25^{\circ})\)
We know that \(\cos(25^{\circ})\approx0.9063\)
So, \(B_x=125\times0.9063 = 113.2875\approx113\space N\)

Answer:

113 N