Answer to Question #159700 in Physics for anna

Question

find the magnitude and the direction of the resultant of the following concurrent and coplanar vectors 80kph, 20° W of N

Answer 1

Consider a vector of 40 kph, 0° W of N, and 80 kph, 20° W of N. Two such vectors (concurrent and coplanar) would produce a resultant vector with x and y components of

$$R_x=0+80\cdot \text{ sin}20°=27.4\text{ kph},\\ R_y=40+80\text{ cos}20°=115\text{ kph}.\\ R=\sqrt{R_x^2+R_y^2}=118\text{ kph}.\\\space\\ \theta=\text{atan}\frac{R_x}{R_y}=13.4°.$$