Question

(problem reference m.1) four displacement vectors are shown in the figure. the magnitudes of the displacements are: $a = 2.25$ cm, $b = 6.35$ cm $= 5.47$ cm, and $d = 4.19$ cm. what is the y - component of vector $vec{d}$? - 2.16 cm - 3.59 cm 2.16 cm 3.59 cm 4.19 cm

Explanation:

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

The formula for the y - component of a vector \(\vec{V}\) with magnitude \(V\) and angle \(\theta\) (measured from the positive x - axis) is \(V_y = V\sin\theta\). For vector \(\vec{D}\), we need to find the angle with respect to the positive x - axis. The angle of vector \(\vec{D}\) with respect to the positive x - axis is \(\theta=180^{\circ}- 31^{\circ}=149^{\circ}\)

Step2: Calculate the y - component of vector \(\vec{D}\)

We know that \(D = 4.19\space cm\) and \(\theta = 149^{\circ}\). Using the formula \(D_y=D\sin\theta\), and \(\sin(149^{\circ})=\sin(180^{\circ}-31^{\circ})=\sin(31^{\circ})\approx0.515\)

$$ D_y=4.19\times\sin(149^{\circ})=4.19\times\sin(31^{\circ})\approx4.19\times0.515 = 2.16\space cm $$

Answer:

\(2.16\space cm\)