a) To find the magnitude of the resultant, we can apply Pythagorean theorem, because vx and vy are the two sides of a rectangle triangle, of which the resultant v is the hypothenuse:
[tex]v= \sqrt{v_x^2+v_y^2}= \sqrt{(7.90)^2+(6.50)^2}=10.2 units [/tex]
b) To find the direction (the angle with respect to the horizontal), let's keep in mind that the tangent of the angle is equal to the ratio between the opposite side and the adiacent side:
[tex]\tan \alpha = \frac{v_y}{v_x}= \frac{-6.50}{7.90}=-0.82 [/tex]
From which we find
[tex]\alpha = arctan (-0.82)=-39.4 ^{\circ}[/tex]
