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{d} )? -2.16 cm 2.48 cm 3.59 cm -4.19 cm -3.59 cm

Explanation:

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

The x - component of a vector \(\vec{D}\) is given by \(D_x=-D\cos\theta\) (negative because the vector is in the second quadrant where x - values are negative). Here, \(D = 4.19\mathrm{cm}\) and \(\theta = 31.0^{\circ}\).

Step2: Calculate the x - component

Substitute the values into the formula: \(D_x=-4.19\times\cos(31.0^{\circ})\).
We know that \(\cos(31.0^{\circ})\approx0.857\).
So, \(D_x=-4.19\times0.857=-3.59\mathrm{cm}\)

Answer:

-3.59 cm