# Relative Motion of Ships

Two ships, A and B, leave port at the same time. Ship A travels northwest at 19 knots and ship B travels at 28 knots in a direction 40° west of south. (1 knot = 1 nautical mile per hour; see Appendix D.)
(a) What is the magnitude the velocity of ship A relative to B?
35.181 knots

(b) What is the direction of the velocity of ship A relative to B?
_____ ° east of north

(c) After what time will the ships be 110 nautical miles apart?
_____ h

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

2. Vab = Vas - Vbs
Vas = -19cos45 + 19sin45 = -13.435i + 13.435j
Vbs = -28cos50 - 28sin50 = -17.998i - 21.449j
Vab = 4.563i + 34.884j
magnitude of Vab = 35.181
arctan(34.884/4.563) = 82.548 degrees

3. For some reason, this value for the angle (which I'm trying to find for part b) is wrong. Any ideas on what I did wrong guys?

jhae2.718
Gold Member
It looks like the problem wants the angle measured East of North. The arctangent function is giving you the angle measured from the horizontal axis (i.e. East).

So, what do you need to do to find the angle as measured from the vertical axis?

Doc Al
Mentor
arctan(34.884/4.563) = 82.548 degrees
I didn't confirm your arithmetic, but you need to express your answer as requested: Degrees east of north.

Oh, right! Thanks a lot guys, I'll try that out.

Edit: It worked! I subtracted the angle from 90 degrees and it was the correct answer

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Now how do I solve part D? I tried adding 180 degrees to the value of the angle for part B, but apparently that's wrong. Any advice?

Doc Al
Mentor
Now how do I solve part D? I tried adding 180 degrees to the value of the angle for part B, but apparently that's wrong. Any advice?
Why add 180 degrees to the answer for part B? It's perfectly OK to swing the velocity vector by 180 degrees, which is probably what you were thinking. Draw a diagram showing their relative positions, then read off the answer.

Once again, be sure to express your answer as requested: Degrees west of south.