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

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Homework Help Overview

The discussion revolves around the relative motion of two ships, A and B, departing from the same port but traveling in different directions and speeds. The problem involves calculating the relative velocity and direction of ship A with respect to ship B, as well as determining the time until they are a certain distance apart and the bearing of ship B relative to ship A at that time.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of relative velocity using vector components and question the correctness of the angle derived from the arctangent function. There is also exploration of how to express angles in the required format, specifically degrees east of north and degrees west of south.

Discussion Status

Some participants have offered guidance on how to adjust the angle calculations to meet the problem's requirements. There is an ongoing exploration of the correct approach for part D, with suggestions to visualize the problem through diagrams and reconsider the angle adjustments.

Contextual Notes

Participants are working under the constraints of specific angle measurements and the requirement to express answers in particular directional formats. There is a noted confusion regarding the arithmetic and the interpretation of angles in relation to the cardinal directions.

Dante Tufano
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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?
 
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Some help anybody? Please
 
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?
 
Dante Tufano said:
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
 
Last edited:
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?
 
Dante Tufano said:
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.
 

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