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Point of slope at certain distance

  1. Sep 8, 2008 #1
    Hey Everyone,

    Another question for you. Is there a way to find the point on a slope at a certain distance? For example, suppose I had a slope that was previously calculated from point A to point B. I want to find at what point Y is at distance X. Does that make sense?
     
  2. jcsd
  3. Sep 8, 2008 #2
    Linear equation?

    y = ax+b

    you can get it from point A and B.

    Slope's not a good work in my opinion. It means finding a point on dy/dx ....
     
  4. Sep 8, 2008 #3

    Dick

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    No, it doesn't really make sense. What's the real question?
     
  5. Sep 8, 2008 #4
    a being point A and b being point B?
     
  6. Sep 8, 2008 #5
    edit: my example doesn't work. I'll post a new example shortly
     
  7. Sep 8, 2008 #6

    Dick

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    Find the equation of the line from A to B and then intersect it with a circle around A of radius X. Is that what you mean? I'm still guessing.
     
  8. Sep 8, 2008 #7
    Ok here's a more precise example:

    I need to calculate the slope from elevation A to elevation B from X1 to X2. Once the slope is determined, the user inputs a distance X3 and a new elevation.

    I need to find the distance between the new elevation and the elevation at point X3 of the original slope.


    Example:

    Find slope from y = 1720.85 feet to y = 1738.34 feet (which starts at x = 2 feet and ends at x = 82 feet).
    Plot this line
    The user inputs a new distance, in this example 64 feet, and a new elevation at 64, 1736.54.
    I need to find the distance between this point (on the new elevation) and the same point (64) on the original slope from A to B.

    Does that make sense?
     
  9. Sep 8, 2008 #8

    Dick

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    That makes perfect sense. Thanks. Why don't you just write an equation for the line whose slope you have computed, i.e. y=m*x+b. Then you just need to compute the vertical distance from new elevation to m*X3+b.
     
  10. Sep 8, 2008 #9
    Thanks for the help.
    I'm a little confused.

    I got a slope of .2186
    Then I do y = .2186(64)+b?
     
  11. Sep 9, 2008 #10

    Dick

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    b is the y-intercept. It value of b that solves .2186*2+b=1720.85. It's just finding the equation of a line through two points. Can you review that?
     
  12. Sep 9, 2008 #11
    I think I did something wrong. I got a distance of 2.1368

    [tex]b=1720.85-.2186*2[/tex]
    [tex]b=1720.4128[/tex]
    [tex]b2=1736.10-.2186*64[/tex]
    [tex]b2=1722.5496[/tex]

    [tex]d = b - b2[/tex]
    [tex]d = 2.1368[/tex]
     
  13. Sep 9, 2008 #12

    Dick

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    If b and b2 are different, it's only because you are rounding off the slope to four decimal places. 1720 and 1736 aren't that different. Try keeping more accuracy around.
     
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