Ship A is sailing towards norht east with velocity `vecv=30hati+50hatj` km/hr where `hati` points east and `hatj`, 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 in _________________hours.

Options

A. 2.2 hrs.
B. 3.2 hrs.
C. 4.2 hrs.
D. 2.6 hrs.

Answer

D

Explanation

Position of B as function of time `= 80 hati + 150 hatj - 10t hati`
Position of A as function of time `30hati + 50t hatj`
`:. Relative position of B as fraction of time = `80hati + 150 hatj - 40t hati - 50t hatj`
Taking magnitude square `=(80 - 40t)^(2) + (150 - 50t)^(2)`
Time derivative = `2(80 -40t)(-40) + 2(150 - 50t) (-50) = 0`
`implies (8-4t)(-4) + (15-5t) (-5) = 0" "implies "16t + 25t = 32 + 75`
`implies 41t = 107 " "implies" " t = 107/41 = 2.6` hrs.