Ship A is sailing towards north – east with velocity ⃗v = 30 î + 50ˆj
km/hr where î points east and ˆj , 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/hr. A will be at minimum distance from B ins:
(A) 2.2 hrs. (B) 4.2 hrs.
(C) 2.6 hrs. (D) 3.2 hrs.
Answers
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Answer:
B = 80 i + 150 j - 10 t i position of B at time t
A = 30 t i + 50 t j position of A at time t
B - A = (80 - 40 t) i + (150 - 60 t) j
| B - A | = (6400 - 6400 t + 1600 t^2 +22500 - 18000 t + 3600 t^2)^1/2
|B - A|^2 = 28900 - 11600 t + 5200 t^2
Take the derivative to find the minimum of |B - A|^2
t = 116 / 52 = 2.2 hrs
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