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November 12th, 2017, 02:41 AM  #1 
Newbie Joined: Nov 2017 From: Serbia Posts: 2 Thanks: 0  Sea ships and their spacetime equations
On different days, two sea ships and their spacetime equations (coordinates in km and hours) were observed: Find out whether the boats have different velocities or different courses. My question: Since the coordinates are time and space, how do I plot these on a graph? Can I do the following: For example for A, can I take 12 as x1 space coordinate and 8 as y1 time coordinate of one point. Then, take 4 and 18 for the other point so that could be the first vector? And how can I calculate the velocity? Thank you. 
November 12th, 2017, 05:22 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,821 Thanks: 750  Quote:
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In any case, rather than using three dimensions to graph A's position, I would say that since x= 12+ 12t, t= (x 12)/12 and then y= 4 4t= 4 4(x12)/12= 4 (x 12)/3= x/3. The graph is y= x/3, a straight line (you could then, mark points on that line with their t value. For example, if t= 0, x= 12, y= 4 so the point (12, 4), which lies on y= x/3, corresponds to t= 0.) Similarly Since, for B, x= 10+10t, t= (x 10)/10. Then y= 2+ 25t= 2+ 25(x 10)/10= 2+ 2.5x 25= 2.5x 27. Notice that those lines have different slopes, 1/3 and 2.5, so they are definitely not the same course. As far as the velocities are concerned they are just the vectors (12, 4) and (10, 25). Of course, 4/12= 1/3 and 25/10= 2.5.  
November 12th, 2017, 06:25 AM  #3 
Newbie Joined: Nov 2017 From: Serbia Posts: 2 Thanks: 0 
Ah, I see. I made a mistake in the equation, it's actually $x = [12 4] +t*[8, 18]$ that's why you couldn't find where it comes from Anyway, it was not correct. Now I understand, I solved the problem Thank you very much! 
November 12th, 2017, 01:56 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,378 Thanks: 542 
the speeds are different  26.9 for B and 19.7 for A. B's speed components have a ratio of 2.5, while A's have a ratio of 2.25, so they are not on the same course.


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equations, sea, ships, spacetime, spacetime, vectors 
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