A man in search of his dog drives first 10 mi northeast then

A man in search of his dog drives first 10 mi northeast, then 24 mi straight south, and finally 1 mi in a direction 30° north of west. What are the magnitude and direction of his resultant displacement?

Solution

Let he start from origin

coordinates after 10 mi northeast = 10*cos(45) i + 10*sin(45) j

coordinates after 24 mi straight south = 10*cos(45) i + 10*sin(45) j -24j

coordinates after 1 mile= 10*cos(45) i + 10*sin(45) j -24j -1cos(30) i + sin(30) j = (10*0.707-0.866)i + ( -24+10*0.707+0.5)

final coordinates => 6.20 i -16.43 j

magnitude = sqrt ( 6.20^2+16.43^2) = 17.56 mile