Find the net displacement of a particle from its starting point if it undergoes two sucessive displacement given by `vecS_(1) = 20m , 37^@` North of West , `vecS_(2) = 50 m, 53^@` North of East.

Explanation

`vecS = vecS_(1) + vecS_(2)`
`S_(x) = S_(1x) + S_(2x)`
`=-20 cos 37^@ + 50 cos 53^@ = 14`
`S_(y) = S_(1y) + S_(2y)`
`=-20 sin 37^@ + 50 sin 53^@ = 52`
`S = sqrt(S_x^2 + S_y^2) = sqrt((14)^(2) + (52)^2) = 53.85`
Angle from west - east axis (x - axis)
`tan theta = (S_y)/(S_x) = 52/14 = 26/7`
`theta = tan^(-1) (26/7)`.