Question

A walker walks through the forest and takes a path that measures 8.0 km in length in a direction of 60.0 degrees @ NE. Continue along path (B) that measures 7.0 km in length in direction @ E. Continuing along path (C) that measures 4.0 km in length in a direction of 315 degrees counterclockwise from the east.

What is the resulting displacement of the walker?

Answer 1

here,

displacement of path A , sA = 8 km * ( cos(60) i + sin(60) j)

sA = 4 km i + 6.928 km j

displacement of path B , sB = 7 km i

displacement of path C , sC = 4 km * ( cos(315) i + sin(315) j)

sC = 2.83 i km - 2.83 km j

the resulting displacement , s = sA + sB + sC

s = 13.83 i km + 4.098 j km

the magnitude , |s| = sqrt(13.83^2 + 4.098^2) = 14.4 km

direction , theta = arctan(4.098/13.83) = 16.5 degree North of East

the resulting displacement is 14.4 km in a direction 16.5 degree North of East