Mike's Yacht, Sailboat Distance Minimization

[thomasrules]

Homework Statement

Mike, who i standing on the deck of a yacth that is traveling due west at 6km/h, sees a sailboat sailing southwestat 4km/h, 3km northwest of the yacht. How close to each other do these boats get?

Homework Equations

The Attempt at a Solution

My drawing is:
| A(2.12-4t,2.12-4t)
| / \
| / \
|/__\B(4.24-6t,0)

Used pythagorean theorem to find t D^2=(2.12-4t-0)^2+(2.12-4t-(4.24-6t))^2

Correct so far?

 

[HallsofIvy]

You have sailboat A with a velocity of <-4, -4>. That gives a speed of
\sqrt{16+ 16}= 4\sqrt{2}, not 4. You need to multiply by
\frac{\sqrt{2}}{2}, just like you did with the initial position.

And it would be a good idea to specifically state, in your final answer, which sailboat is A and which B and how your coordinate system is set up.