Question

required information
four vectors are shown below, where ( l = 8.00 ).
find the ( x )-component of the vector ( vec{d} ).
\boxed{} m/s

Explanation:

Step1: Identify vector direction

Vector $\vec{D}$ has magnitude $l=8.00\ \text{m/s}$, and is $20.0^\circ$ to the left of the negative y-axis, so its angle from the positive x-axis is $270^\circ - 20.0^\circ = 250^\circ$.

Step2: Calculate x-component

Use the formula for x-component of a vector: $D_x = |\vec{D}| \cos\theta$
<Expression>
$D_x = 8.00 \times \cos(250.0^\circ)$
$\cos(250.0^\circ) = \cos(180^\circ+70^\circ) = -\cos(70^\circ) \approx -0.3420$
$D_x = 8.00 \times (-0.3420) = -2.736$
</Expression>

Answer:

$-2.74\ \text{m/s}$ (rounded to three significant figures)