A commuter airplane starts from an airport and takes the routeshown in fig. p3.1

Question

A commuter airplane starts from an airport and takes the routeshown in fig. p3.13. the plane first flies to city A, located 275km away in a direction 30.0 degrees north of east. Next it fliesfor 170.0 km in a direction of 20.0 degrees west of north, to cityB. Finally, the plane flies 140.0km due west to city C relative tothe location of the starting point. a) first find the linear distance from the starting point tocity C, in km. b) how many degrees north of east muct the plane fly? Please show me step by step A commuter airplane starts from an airport and takes the routeshown in fig. p3.13. the plane first flies to city A, located 275km away in a direction 30.0 degrees north of east. Next it fliesfor 170.0 km in a direction of 20.0 degrees west of north, to cityB. Finally, the plane flies 140.0km due west to city C relative tothe location of the starting point. a) first find the linear distance from the starting point tocity C, in km. b) how many degrees north of east muct the plane fly? Please show me step by step

Explanation / Answer

Let north be pos y, south neg y, east pos x, west neg x break each flight into x and y i)275km 30 deg north of east so x=275cos(30)=238.16km y=275sin(30)=137.5km ii)170km 20 deg west of north x=-170sin(20)=-58.14km y=170cos(20)=159.75km iii)140km west x=-140km y=0km add up total x and y, total x=40.02km=40.02km East total y= 297.25km North distance =sqrt(x2+y2)=sqrt(40.022+297.252)=299.93km tan=opp/adj=y/x=297.25/40.02, =82.33 degrees The plane must fly 299.93km 82.33 degrees North ofEast

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