Thread: Optimization-Ship Distance question

This question is frustrating me I tried it 10 times... not sure what i am doing wrong help would be much appreciated.

A ship is sailing due north at 12 kn when it observes another ship dead ahead at a distance of 15 n. mi. The second ship is sailing due east at 9 kn. What is the closest distance of approach of the two ships?

Originally Posted by Calculus23

This question is frustrating me I tried it 10 times... not sure what i am doing wrong help would be much appreciated.

A ship is sailing due north at 12 kn when it observes another ship dead ahead at a distance of 15 n. mi. The second ship is sailing due east at 9 kn. What is the closest distance of approach of the two ships?

let the northbound ship start at (0,0)

let the eastbound ship start at (0,15)

northbound ship's position (x,y) as a function of time, t , in hrs ...

(0,12t)

eastbound ship's position (x,y) as a function of time ...

(9t,15)

use the distance formula to set up an expression for the distance between the two ships as a function of time ... take the time derivative and minimize.

How do i set up the expression :S

Originally Posted by Calculus23

How do i set up the expression :S

what is the distance formula between two points in a plane?