Question

draw each of the following vectors then find its x and y component. a. a = 3.5 m/s^2, negative x directionb. v = 440 m/s, 30° below the positive x-axisc. r = 12 m, 40° above the positive x-axis

Answer 1

Drawing the vectors, we have:

Now, calculating the components of each vector:

$\begin{gathered} a_x=a\cdot\cos (180\degree)=3.5\cdot(-1)=-3.5 \\ a_y=a\cdot\sin (180\degree)=3.5\cdot0=0 \\ \\ v_x=v\cdot\cos (-30\degree)=440\cdot0.866=381 \\ v_y=v\cdot\sin (-30\degree)=440\cdot(-\frac{1}{2})=-220 \\ \\ r_x=r\cdot\cos (40\degree)=12\cdot0.766=9.19 \\ r_y=r\cdot\sin (40\degree)=12\cdot0.6428=7.71 \end{gathered}$