Question

A boat sails 100 km east than 200 km 60^o south of east. How far and which way is it from the origin?

Answer 1

let +x axis be East.
and +y axus be North.

A = 100 km
B = 200 km

x-component of resultant displacement,

Rx = Ax + Bx

= 100 + 200*cos(60)

= 200 km

y-component of resultant displacement,

Ry = Ay + By

= + (-200*sin(60))

= -173 km

resultant displacement, R = sqrt(Rx^2 + Ry^2)

= sqrt(200^2 + 173^2)

= 264 km <<<<<<<<<------------Answer

direction : theta = tan^-1(Ry/Rx)

= tan^-1(-173/200)

= 40.9 degrees south of east <<<<<<<<-----------Answer