Question

an explore in the dense jungles of equatorial Africa leaves his hut.he takes 40 steps northeast,then 80 steps 60 degrees north of west,then 50 steps due south.assume his steps all have equal length.save him from becoming hopelessly lost in the jungle by giving him the displacement,calculated using the method of components,that will return him to his hut.

Answer 1

Let us break the displacement components along 'north' and along 'east'.

\(40 \ steps \ northeast\)
Displacement along east = \(\large{d_{e1}}\)=40 cos45=28 steps
Displacement along north = \(\large{d_{n1}}\)=40 sin45=28 steps

\(80 \ steps \ 60 \ degrees north \ of \ west\)
Displacement along east = \(\large{d_{e2}}\)=-80 cos60=-40 steps {- says man moves to west}
Displacement along north = \(\large{d_{n2}}\)=80 sin60=69 steps

\(50 \ steps \ south\)
Displacement along east = \(\large{d_{e3}}\)=0 steps
Displacement along north = \(\large{d_{n3}}\)=-50 steps {- says man moves south}

Total displacement along east = \(\large{d_{e}}\)=28-40 =-12 steps
Displacement along north = \(\large{d_{n}}\)=28+69-50=47 steps

So, that guy is 47 steps north and 12 steps west from his hut.