 Good morning friends, I am Pooja and today we will work out the following question a girl walks four kilometer towards West Then she walks three kilometer in a direction 30 degree east of north and stops Determine the girls displacement from her initial point of departure Let us begin with the solution now Now with the help of the given information we draw the following figure now in this figure We have oh a is equal to four kilometer AP is equal to three kilometer and Angle oh a P is equal to 60 degree We draw Pm perpendicular to oh a then in triangle a Pm we have Am is equal to three cost 60 degree This is equal to three into one upon two because cost 60 degree is equal to one upon two So we get a m is equal to three upon two Therefore we have O m is equal to O a minus a m Which is equal to now o a is equal to four kilometer So we have four minus a m is equal to three upon two And we get this is equal to five upon Two so we have got o m is equal to five upon two now again in triangle a Pm we have Pm is equal to Three sign 60 degree This is equal to three into root three upon two Because sign 60 degree is equal to root three upon two so we get Pm is equal to three root three upon two Now we have to find girls displacement from her initial point of departure That is we have to find vector OP now applying triangle law in Triangle OPM we have Vector OP is Equal to vector o m Plus vector MP This is equal to now vector O m is equal to five upon two so we have five upon two Now we know that along x axis the unit vector is I cap now O m is moving in opposite direction. So we have minus I cap So we get minus five upon two I cap plus Now vector MP is equal to three root three upon two and Along y-axis the unit vector is J cap and MP is moving along the same direction So we get plus three root three upon two J cap Hence the girls displacement from the initial point of departure that is vector OP is equal to Minus five upon two I cap plus Three root three upon two J cap this is our answer. Hope you have understood the solution. Bye and take care