Problem 1: Problem 1.58 in Young & Freedman A plane leaves the airport in Galisteo and flies 170 km at 68.0° east of north; then it changes direction to fly 230 km at 36.0° south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

We shall convert the displacement in vector form using unit vector i and j

consider east as x axis and north as y axis

170 km at 68.0° east of north

D₁ = 170 sin68 i + 170cos 68 j

= 157 i + 63.68 j

230 km at 36.0° south of east

D₂ = 230 cos36 i - 230 sin 36 j

= 186 i - 135.2 j

Resultant Displacement = D₁ + D₂

= 157 i + 63.68 j + 186 i - 135.2 j

= 343 i - 71.52 j

Resultant magnitude

= √ (343² + 71.52²

= 350 km

Angle

= tan⁻¹ ( - 71.52 / 343)

12⁰ south of east.