Question

question 10
(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{c} ) ?
( 3.59 mathrm{~cm} )
( 4.87 mathrm{~cm} )
( -2.48 mathrm{~cm} )
( 5.47 mathrm{~cm} )
( 2.48 mathrm{~cm} )

Explanation:

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

The formula for the x - component of a vector \(\vec{C}\) is \(C_x = C\sin\theta\), where \(C\) is the magnitude of the vector and \(\theta\) is the angle with respect to the y - axis.

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

Given \(C = 5.47\space cm\) and \(\theta=27.0^{\circ}\)

Step3: Calculate the x - component

Substitute the values into the formula: \(C_x=5.47\times\sin(27.0^{\circ})\)
We know that \(\sin(27.0^{\circ})\approx0.454\)
\(C_x = 5.47\times0.454\approx2.48\space cm\)

Answer:

\(2.48\space cm\)