Question

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

Explanation:

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

The formula for the y - component of a vector \(\vec{B}\) with magnitude \(B\) and angle \(\theta\) (measured from the \(x\) - axis) is \(B_y=B\sin\theta\).

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

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

Step3: Calculate \(B_y\)

Substitute the values into the formula: \(B_y = 125\times\sin(25.0^{\circ})\)
Since \(\sin(25.0^{\circ})\approx0.4226\), then \(B_y=125\times0.4226 = 52.825\approx52.8\space N\)

Answer:

\(52.8\space N\) (corresponding to the fourth option)