How Do Ships A and B Move Relative to Each Other?

[Jharr94]

Homework Statement

Two ships, A and B, leave port at the same time. Ship A travels northwest at 22 knots and ship B travels at 29 knots in a direction 40° west of south.

(a) What is the magnitude the velocity of ship A relative to B?

(b) What is the direction of the velocity of ship A relative to B?

(c) After what time will the ships be 125 nautical miles apart?

(d) What will be the bearing of B (the direction of B's position) relative to A at that time?

Homework Equations

V_aw=V_ab+V_b Where a is boat a, b is boat b, and w is the water-also aw is ship a's velocity with respect to the water, ab is the velocity of a with respect to b)

The Attempt at a Solution

I found the componets of the two vectors(with respect to a y-axis that's positive in the north direction and an x-axis positive in the east direction) as:
A=(-15.55i+15.55j) or (22cos45+22sin45)
B=(-22.22i+-18.64j) or (29cos40+29sin40)

I've found these componets with respect to their own frames of reference, however the problems asks for the magnitude of the velocity of a with respect to b, so should I measure my angles of a from the b vector? I'm lost as to how to solve. Also I've come to the conclusion that this is addition( or subtraction) of vectors a and b, being that its a with respect to b however I'm not sure if it is B-A=C (with c being the velocity of a with respect to b)or A-B=C.

 

[Jharr94]

So I'm looking for V_ab( velocity of a with respect to b), therefore the velocity of a(V_a) is equal to the velocity of b(V_B) plus the velocity of a with respect to b(V_ab) and I know both a and b so:

V_a=V_ab+V_b

22=V_ab+29

-7=V_ab

however is is showing as incorrect(I used 7 since it asked for the magnitude)

 

[Jharr94]

I also tried the vector equations:

(V_ax+V_ay)=(V_abx+V_aby)+(V_bx+V_by)

or

(-15.55i+15.55j)=(V_abx+V_aby)+(-22.22i+18.64j)

so when I separate the equations I get:

-15.55=V_abx-22.22

V_abx=6.67i

15.55=V_aby+18.64

V_aby=-3.09

therefore V_ab=(6.67i+3.09j)
so the magnitude of V_ab should be 7.35
Right?

 

[Jharr94]

I really need help with this, its due in a few hours. =/

 

[tiny-tim]

Welcome to PF!

Two ships, A and B, leave port at the same time. Ship A travels northwest at 22 knots and ship B travels at 29 knots in a direction 40° west of south.
…
B=(-22.22i+-18.64j) or (29cos40+29sin40)

Hi Jharr94! Welcome to PF!

West of south is between southwest and south.

You're using south of west.