First, let's add the vectors:
[tex]v=v_1+v_2=(-50i+4j)+(5i+15j)=-45i+19j[/tex]
The true speed is given by the magnitude of the resulting vector:
[tex]|v|=\sqrt{(-45)^2+(19)^2}=\sqrt{2025+361}=\sqrt{2386}=48.847[/tex]
The direction can be calculated with the formula below:
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{19}{-45})\\ \\ \theta=157° \end{gathered}[/tex]
Therefore the correct option is the first one.
