distance problem

euclid2

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
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 $$\displaystyle d$$.

HallsofIvy