Question

Angelo was observing an ant that crawled along a tabletop. With a piece of chalk, he followed its path. He determined the ant's displacements by using a ruler and protractor. The displacements as follows: 3.0 cm, east; 2.5 cm, 30 degrees north of east; 1.5 cm, 30 degrees west of north. Where is the final location of the ant? Use graphical method. Show your solution.

Answer 1

 final location:

x-coordinate:

$x=3+2.5cos30\degree-1.5sin30\degree=2.25+1.25\sqrt3$

y-coordinate:

$y=2.5sin30\degree+1.5cos30\degree=1.25+0.75\sqrt3$

distance from start to final location:

$l=\sqrt{x^2+y^2}=\sqrt{9.75+3.25}=\sqrt{13}$

direction from start to final location:

$\theta=arctan(y/x)=arctan(y/x)=30\degree$ north of east