ANSWER:
43.68 m/s with a direction of 74.05°
STEP-BY-STEP EXPLANATION:
We make the sketch of the situation, just like this:
We can calculate the magnitude of the resulting velocity just like this (By means of the Pythagorean theorem since a right triangle is formed):
[tex]\begin{gathered} h^2=a^2+b^2\rightarrow h=\sqrt{a^2+b^2} \\ \\ V_{R}=42^{2}+12^{2} \\ \\ V_R=\sqrt{1764+144} \\ \\ V_R=\sqrt{1908} \\ \\ V_R=43.68\text{ m/s} \end{gathered}[/tex]While the direction is calculated as follows (applying the tangent trigonometric ratio):
[tex]\begin{gathered} \tan\theta=\frac{V_{north}}{V_{east}} \\ \\ \text{ We replacing} \\ \\ \tan\theta=\frac{42}{12} \\ \\ \theta=\tan^{-1}\left(\frac{42}{12}\right)\: \\ \\ \:θ=74.05\degree \end{gathered}[/tex]Which means that the resulting velocity is 43.68 m/s with a direction of 74.05°
