Question

(problem reference m.1) four displacement vectors are shown in the figure. the magnitudes of the displacements are: ( a = 2.25 mathrm{~cm}, b = 6.35 mathrm{~cm}, c ) ( = 5.47 mathrm{~cm} ), and ( d = 4.19 mathrm{~cm} ). what is the ( x )-component of vector ( vec{a} )? ( 1.17 mathrm{~cm} ) ( 1.39 mathrm{~cm} ) ( -1.59 mathrm{~cm} ) ( -2.17 mathrm{~cm} ) ( 2.25 mathrm{~cm} )

Explanation:

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

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

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

We are given that \(A = 2.25\space cm\) and \(\theta=52.0^{\circ}\).

Step3: Calculate the x - component

Substitute the values into the formula: \(A_x = 2.25\times\cos(52.0^{\circ})\).
We know that \(\cos(52.0^{\circ})\approx0.6157\).
So, \(A_x=2.25\times0.6157 = 1.39\space cm\)

Answer:

\(1.39\space cm\)