Ateacher sends her students on a treasure hunt. she gives the following instructions: · walk 300 m north · walk 400 m northwest · walk 700 m east-southeast and the treasure is buried there. as all the other students walk off following the instructions, jane physics student quickly adds the displacements and walks in a straight line to find the treasure. how far (in meters) does jane need to walk?

displacement is 481.3 m  with 40.88° north east

Explanation:

given data

walk 1 = 300 m north = 300 j

walk 2 = 400 m northwest =400 cos(45) i + sin(45) j

walk 3 = 700 m east southeast  = 700 cos(22.5) i- sin(22.5) j

to find out

displacement and direction

solution

we consider here direction x as east and direction y as north

so

displacement = distance 1 + distance 2 + distance 3

displacement = 300 j + 400 cos(45) i + sin(45) j + 700 cos(22.5) i- sin(22.5) j  

we get here

displacement = 363.9 i + 315 j

so magnitude

displacement =

displacement = 481.3 m

and angle will be = arctan(315/369.9)

angle = 0.713494059 rad

angle is 40.88 degree

so displacement is 481.3 m  with 40.88° north east