Question about 2 ships - vectors?

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Homework Help Overview

The problem involves two ships departing from a port and traveling in different directions at specified speeds. The context is centered around vector analysis to determine the distance between the ships and the relative speed of one ship as observed from the other.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of vectors to represent the ships' movements, suggesting the drawing of vectors at specified angles. There is mention of applying the law of cosines to find the distance between the ships. Questions arise regarding the interpretation of relative speed as seen from one ship to another.

Discussion Status

Some participants have successfully calculated part A of the problem and are now exploring how to approach part B. There is an ongoing clarification about the concept of relative speed and how it applies in this context.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on understanding vector representation and relative motion.

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Homework Statement



Ships A and B leave port together. For the next two hours, ship A travels at 35 mph in a direction 20° west of north while the ship B travels 10° east of north at 40 mph.

(a) What is the distance between the two ships two hours after they depart (in miles)?


(b) What is the speed of ship A as seen by ship B (in mph)?


Homework Equations





The Attempt at a Solution



I have no idea how to approach this problem. I believe it is vectors, however as I said I'm not sure. Any help would be greatly appreciated.
 
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Start by drawing 2 vectors from one point, let's say (0,0)
-One vector will go at a 20° angle to the west (of north) and the other will go 10° east (of north)
-Since it's 2 hours you can make the vector length double (70 and 80).
-You will end up have 1 angle, 2 sides
-You can now use the law of cosines to solveI believe this is correct, if not someone will correct me :p

Edit: that's part A.
 
Thank you, that made a lot of sense and I calculated part A correct. How would I calculate part B though? What does speed as seen by the other mean?
 
Pretend you were standing on boat B watching boat A. If both boats were traveling in tje same direction at the same speed, boat A would appear stationary to someone on boat B.
 

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