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Formula for vertical and horizontal components of trajectory

Discussion in 'General Gun Discussions' started by Oleg Volk, Aug 9, 2006.

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  1. Oleg Volk

    Oleg Volk Moderator Emeritus

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    I need to come up with a formula for x and y coordinates of a ballistic projectile, neglecting air resistance. I forgot most of my physics and math, so I'd like to verify my guesses:

    for vertical position (sinLAUNCH ANGLE * velocity - FREEFALL ACCELERATION * time) * time
    for horizontal cosineLAUNCH ANGLE * velocity * time

    Thanks in advance...
     
  2. Gonefission

    Gonefission Member

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  3. Oleg Volk

    Oleg Volk Moderator Emeritus

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    I looked through that page earlier. Let's look here:

    d937be7f39b6e438b5e9a37da16db59b.png

    v = velocity?
    g = freefall acceleration?

    And how do I find x? Is my original formula for that correct?

    Update:

    My father just emailed me the correct formula:

    Almost right...
    for vertical position (sinLAUNCH ANGLE * velocity - FREEFALL ACCELERATION * time / 2) * time reflecting that (sinLAUNCH ANGLE * velocity - FREEFALL ACCELERATION * time) is the vertical speed at that time but the average one was half of that.
     
  4. Gonefission

    Gonefission Member

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    Here is the legend from the top of that page:


    According to my TI-89 solving for x gets you the attached formula
     

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  5. WayneConrad

    WayneConrad Member

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    Oleg, if you're shooting on the moon, remember that you'll need a different value for g.

    This could be the coolest range report ever.
     
  6. johnmcl

    johnmcl Member

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    Simpler Version

    Hi Oleg,

    That last equation doesn't take into consideration a couple of trig properties that will simplify your work.

    Essentially Range = V^2 sin(2*angle)/g

    There's a great astrophysics page here that has done the mathematical heavy lifting:

    http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

    Now a couple of points. Express your angle in radians, and the effect of gravity (g) as 32 ft/sec^2. That will allow you to keep your muzzle velocity in feet per second.

    Hope that helps?

    John
     
  7. roo_ster

    roo_ster Member

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    Here's how I always did my work in English measurements:
    1. Convert given data into mks
    2. Solve equation via algebra/trig/calc
    3. Plug in mks values & solve
    4. Convert to English measurements

    I love English measurements for everday life, but I want metric for engineering/physics/tech work.
     
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