Question

As preparation for this problem, consult Concept Simulation 1.1. On a safari, a team of naturalists sets out toward a research station located 6.14 km away in a direction 31.3 ° north of east. After traveling in a straight line for 1.67 km, they stop and discover that they have been traveling 8.50 ° north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (as a positive angle relative to due east) of the displacement vector now required to bring the team to the research station? (a) Number Units (b) Number Units

Answer 1

let x and y axis are along east and north respectively.

let i and j are unit vectors along x and y axis respectively.

then position of the research station=6.14*(cos(31.3) i + sin(31.3) j)

=5.2464 i + 3.1898 j

position after journey for 1.67 km

=1.67*(cos(8.5) i+ sin(8.5) j)

=1.65166 i +0.24684 j

so displacement required=position of the research station-their current position

=(5.2464 i + 3.1898 j)-(1.65166 i +0.24684 j)

=3.5947 i + 2.943 j

so magnitude of displacement required=sqrt(3.5947^2+2.943^2)

=4.6458 km

angle with east=arctan(2.943/3.5947)

=39.307 degrees