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## 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

_{B}V

_{A}= 12i - 12j

V

_{B}

=

_{B}V

_{A}+ V

_{A}

=12i - 5j

so θ = tan

^{-1}5/12 = 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?