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, c = 5.47 cm, and d = 4.19 cm. what is the x - component of vector \\( \vec { b } \\)? 2.17 cm 4.87 cm 5.97 cm 6.35 cm - 2.17 cm

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 \(\theta\)

We are given that \(B = 6.35\space cm\) and \(\theta=20.0^{\circ}\)

Step3: Calculate the x - component

Substitute the values into the formula:
\(B_x = 6.35\times\cos(20.0^{\circ})\)
We know that \(\cos(20.0^{\circ})\approx0.9397\)
\(B_x=6.35\times0.9397\approx5.97\space cm\)

Answer:

\(5.97\space cm\)