Vector (Relative velocity question)

[Michael_Light]

1. The problem statement, all variables and given/known data

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.

2. Relevant equations



3. The attempt at a solution

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

Now, VA = 7j

BVA = 12i - 12j

VB
= BVA + VA
=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.