Question

The three finalist in a contest are brought to the center of a large flat field. calculate the following displacements:
72.4 m, 32^o east of south
57.3 m, 36^o south of west
17.8 m straight south
What is the magnitude and direction of the resultant?

Answer 1

$A(x,y)=(72.4\sin32°,72.4\cos32°)=(38.4m,-61.4m)$

$B(x,y)=(57.3\cos36°,57.3\sin36°)=(-46.4m,-33.7m)$

$C(x,y)=(0m,-17.8m)$

$\sum{x}=38.4-46.4=-8m$

$\sum{y}=-61.4-33.7-17.8=-112.9m$

$Displacement=\sqrt{8^2+112.9^2}=113.2(m)$

$Direction=\tan^{-1}{\frac{112.9}{8}}=85.9°$ south of west.