While playing a scavenger hunt game, Anthony walks 48.0 m to the south and then walks 12.0 m to the west. What single straight-line displacement could Anthony have taken to reach this point? (Use trigonometry to answer, but remember to draw a diagram to help your understanding.) Give both the magnitude and the angle in your answer.
Answer:
Anthony walks 48 m to the south and then 12 m to the west.
so , lets assume a co-ordinate plane, Let O be the origin, then +y will represent North direction,-y will represent South direction ,+x will represent East , -x will represent West direction.
So, according to the problem we will sketch the path,48 m towards -y (say point A)and then 12m towards -x (say point B).B is the final destination.
so OB is the displacement ,and angle AOB is the direction.
So AB=12m=perpendicular
OA=48 m = base
OB= hypotenuse= displacement.
By pythagoras theorem
.hypotenuse^{2}=perpendicular^{2}+base^{2}
OB=49.47m
so tan(x)=perpendicular/base=AB/OA=12/48
x=tan^-1(.25)=14.04
Direction = S14.04W