- #1

- 56

- 0

## Homework Statement

Consider a Cartesian coordinate system, with units measured in 1000 feet, and with the z = 0 coordinate plane lying on the ocean surface. Two ships A and B, moving at speed 250 feet/min, are located at (4,0,0) and (0,5,0), moving North (-x direction) and West (-y direction) and detect a submarine in the directions <2, 3, -1/3> and <18, -6, -1>, respectively at t = 0 minutes. Four minutes later the detected directions by A and B are <9,9,-1> and <18,-3,-1> respectively. The ships guide an intercept of the submarine. What coordinates should be given the attacking aircraft that is due at t = 20 if the submarine is assumed to move along a straight line and constant speed?

## Homework Equations

All vector operations? Addition, multiplication.

Possibly length of vectors.

## The Attempt at a Solution

Ok i'm not sure if i completely understand this problem especially when it says "detect a submarine in the directions <2,3,-1/3>" does this mean that the submarine is that many units away from ship A? If this is the meaning then that would mean the at t = 0 the submarine is at <6, 3, -1/3> However, I don't think this is the case because when I use the same reasoning to find the position of the submarine in relation to ship B I get <18, -1, -1> which doesn't make any sense. I don't think this problem is very difficult I just need to figure out the [tex]\vec{v}[/tex] of the submarine and calculate where it will be at t = 20. I just aren't sure how to go about finding its velocity vector.