Question

a force vector shown below has a magnitude of 14 newtons. the force vector is at an angle of 56 degrees from the x axis. determine the magnitude of the y component of the force vector.

Explanation:

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

The formula for the y - component \(F_y\) of a vector \(\vec{F}\) with magnitude \(F\) and angle \(\theta\) (measured from the x - axis) is \(F_y=F\sin\theta\).
Here, \(F = 14\space N\) and \(\theta=56^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(F = 14\) and \(\theta = 56^{\circ}\) into the formula \(F_y=F\sin\theta\).
We know that \(\sin(56^{\circ})\approx0.8290\).
So, \(F_y=14\times\sin(56^{\circ})\approx14\times0.8290 = 11.606\space N\).

Answer:

The magnitude of the y - component of the force vector is approximately \(11.6\space N\) (or more precisely \(14\sin(56^{\circ})\approx11.6\space N\)).