Hiker Vectors

Question

A hiker begins a trip by first walking 19.6 km southeast from her base camp. On the second day, she walks 41.2 km in a direction 63.7 north of east, at which point she discovers a forest ranger's tower. Determine the y component of total displacement.

 

Answer in units of km

 

Answer 1

 

Take North y(positive axis) ,South y(negative axis)

East x(positive axis) ,West x(negative axis)

Frist He went south east .i.e making -45^o degree with positive x axis.Then He turned 63.7^o degree clockwise from x axis.

So the Y component o the displacement is

41.2*sind(63.7^o)-19.6*sin(45^o)= 23.076 km North

So the X component o the displacement is

41.2*cosd(63.7)+19.6*cosd(45)== 32.114 km east

 

 

Answer 2

To answer this question, imagine a coordinate plane with north, south, east, west.  Then when she mocves south east, assume she moves at -45 degree angle with a vector length of 19.6.  This yields an isosceles right  triangle with hypotenuse 19.6 km.  Then find the side lengths of this triangle.  Using Pythagorean theorem, the side lengths are 13.9.  She moved down 13.9 miles (first y component of displacement).  Secondly, from this position, she moved NE 41.2 miles which creates a right triangle with angle 63.7 degrees and hypotenuse 41.2.  Using the relation: sin(63.7) = x/41.2 tells us the length of the opposite side (the y displacement).  Solving for x yields x=31.44.  Total displacement = 31.44-13.9 = 17.54 km