Ship A is sailing towards north-east with velocity ⃗v = (30̂i + 50̂j) km h⁻¹ where ̂i points east and ̂j, north. Ship B is at a distance of 80 km east and 150 km north of ship A and is sailing towards west at 10 km h⁻¹. A will be at minimum distance from B in

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(4) 2.6 h. Work relative to A. Position of B: ⃗r = (80, 150) km. Velocity of B relative to A: ⃗u = (-10 - 30, 0 - 50) = (-40, -50) km/h. Separation ⃗r + ⃗u t is smallest when it is perpendicular to ⃗u: (⃗r + ⃗u t)·⃗u = 0. t = -(⃗r·⃗u)/(|⃗u|²) = (3200 + 7500)/(1600 + 2500) = (10700)/(4100) = 2.6 h.

Ship A is sailing towards north-east with velocity ⃗v = (30̂i + 50̂j) km h⁻¹ where ̂i points east and ̂j, north. Ship B is at a distance of 80 km east and 150 km north of ship A and is sailing towards west at 10 km h⁻¹. A will be at minimum distance from B in

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