A ship leaves the island of Guam and sails a distance 255 km at an angle 49.0 o north of west. Part A: In which direction must it now head so that its resultant displacement will be 125 km directly east of Guam? (Express your answer as an angle measured south of east) Part B: How far must it sail so that its resultant displacement will be 125 km directly east of Guam?

We shall represent displacement in vector form. Consider east as x axes and north as Y axes west as - ve x axes and south as - ve Y axes. 255 km can be represented by the following vector

D₁ = - 255 cos 49 i + 255 sin49 j

= - 167.29 i + 192.45 j

Let D₂ be the further displacement which lands him 125 km east. So the resultant displacement is

D = 125 i

So

D₁ + D₂ = D

- 167.29 i + 192.45 j + D₂ = 125 i

D₂ = 125 i + 167.29 i - 192.45 j

= 292.29 i - 192.45 j

Angle of D₂ with x axes θ

tan θ = - 192.45 / 292.29

= - 0.658

θ = 33.33 south of east

Magnitude of D₂

D₂² = (192.45) ² + (292.29) ²

D₂ = 350 km approx

Tan