Ship A sails north-east with velocity (30î+50ĵ) km h⁻¹, where î is east and ĵ is north. Ship B is initially 80 km east and 150 km north of A and sails west at 10 km h⁻¹. After how much time will A be at minimum distance from B?
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Question

Ship A sails north-east with velocity (30î+50ĵ) km h⁻¹, where î is east and ĵ is north. Ship B is initially 80 km east and 150 km north of A and sails west at 10 km h⁻¹. After how much time will A be at minimum distance from B?

Options

G1 Physics · Accepted Answer

Initial relative position of B from A is r₀=80î+150ĵ km. vₐ=30î+50ĵ and vᵦ=-10î, so vᵦₐ=-40î-50ĵ. Closest approach occurs at t=-(r₀·vᵣ)/|vᵣ|² =-[80(-40)+150(-50)]/(40²+50²)=10700/4100≈2.61 h. Hence option D.