# Minimize Distance

1. Jan 17, 2007

### thomasrules

1. The problem statement, all variables and given/known data
Mike, who i standing on the deck of a yacth that is travelling 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?

2. Relevant equations

3. 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?

Last edited: Jan 17, 2007
2. Jan 18, 2007

### 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.