Vector (Relative velocity question)

[Michael_Light]

Homework Statement

An observer, on a ship A sailing to the north with speed of 7km/h, saw a ship B. Ship B seems to be moving to south-east with a speed of 12√2 km/h.

Find the direction which B is heading to.

Homework Equations

The Attempt at a Solution

Let i and j be the unit vectors in the direction of eat north respectively and V_A = velocity of ship A and V_B = velocity of ship B.

Now, V_A = 7j

_BV_A = 12i - 12j

V_B
= _BV_A + V_A
=12i - 5j

so θ = tan^-15/12 = 22.6°

The direction of ship B is E22.6°S.

But the answer given is N67°23'E, which step is incorrect? Can anyone enlighten me?

 

[Doc Al]

The direction of ship B is E22.6°S.

But the answer given is N67°23'E, which step is incorrect? Can anyone enlighten me?

Your answer looks fine to me. Are you sure the book's answer wasn't S67°23'E, which would be pretty close to yours.