At 1300 hours a merchant ship sailing south at 18 knots is 40 nautical miles due east of a patrol boat travelling east at 24 knots. When will they be closest to each other?
Answer: 14:04
Thank you for any help.
At 1300 hours a merchant ship sailing south at 18 knots is 40 nautical miles due east of a patrol boat travelling east at 24 knots. When will they be closest to each other?
Answer: 14:04
Thank you for any help.
$t=0$ is 1300
let the patrol boat's initial position be the origin, (0,0)
patrol boat's position at any time $t$ is $(24t,0)$
merchant ship's initial position is (40,0)
merchant ship's position at any time $t$ is $(40,-18t)$
distance between the two at any time $t$ ...
$d = \sqrt{(24t-40)^2 + [0-(-18t)]^2} = \sqrt{900t^2-1920t+1600}$
minimum distance will occur at the minimum value of the parabola, $900t^2-1920t+1600$, located at its vertex
when $t = \dfrac{-b}{2a} = \dfrac{1920}{2 \cdot 900} = \dfrac{16}{15} \, hrs = 1 \, hr \, 4 \, min$
time of CPA is 1404