This question has several parts that must be completed sequentially. If you skip

Question

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not race not be able to come back to the skipped part. A boat leaves a dock at 2:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 PM How many minutes after 2:00 PM were the two boats closest together? Let t be the time, In hours, after 2:00 PM If the position of the boat at t = 0 corresponds to the origin, then the position of the boat heading south at time t is (x, y) = (

Explanation / Answer

At any time t hrs after 2 PM,
let 'd' be the distance between both boats.
Using Pythagoras theorem:
d^2 = (15-15t)^2 + (20t)^2
d^2 = 225(1-t)^2 + 400t^2
d^2 = 625t^2 - 450t +225

minimising d^2 would also minimise d, so taking derivative & equating to zero,

1250t - 450 = 0,

t = 9/25 hr = 21.6 min after 2 PM

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