distance problem

May 2008
400
82
Ottawa, Canada
a boat leaves a dock at 2.pm, heading west at 15km/h. another boat heads south at 12km/h and reaches the same dock at 3.pm when were the boats closest?
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
a boat leaves a dock at 2.pm, heading west at 15km/h. another boat heads south at 12km/h and reaches the same dock at 3.pm when were the boats closest?
let the dock be at the origin.

let t = 0 be 2pm

west boat's position \(\displaystyle (x,y)\) as a function of time ...

\(\displaystyle (-15t,0)\)

south boat's position \(\displaystyle (x,y)\) as a function of time ...

\(\displaystyle (0, 12 - 12t)\)

use the distance formula and minimize ... to make it easy, note that if you minimize \(\displaystyle d^2\) , you also minimize \(\displaystyle d\).
 
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