we are given a vector
whose
x-component is -24.5
so, [tex]v_x=-24.5[/tex]
y-component is 31.5
so, [tex]v_y=31.5[/tex]
Magnitude:
we can use formula
[tex]|v|=\sqrt{(v_x)^2+(v_y)^2}[/tex]
we can plug values
[tex]|v|=\sqrt{(-24.5)^2+(31.5)^2}[/tex]
[tex]|v|=39.90614[/tex]
Direction:
we can use direction formula
[tex]\theta=tan^{-1}(\frac{v_y}{v_x})[/tex]
now, we can plug values
[tex]\theta=tan^{-1}(\frac{31.5}{-24.5})[/tex]
[tex]\theta=180-52.12[/tex]
[tex]\theta=127.88[/tex]................Answer
