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Projectile Motion: finding velocity if given range, angle, and height.

  1. Mar 13, 2012 #1
    Hey everyone!
    I have been asked to find an equation with the subject of V (initial speed) with only the information given, angle above horizontal, range, and initial height above ground. I did attempt this myself and got the formula:
    v = initial speed
    θ = initial angle
    s = range (total)
    h = initial height above ground

    v3(2s*tanθ) + v2(2h) + s2/cos2θ = 0

    It is a cubic and so I left it in this form but I found this to be incorrect (will not show working as it is around a page) and have been over my work multiple times. Please help me with this!
  2. jcsd
  3. Mar 13, 2012 #2
    Nevermind, with hard work and starting from scratch I managed to derive this formula!!!!!:

    v = initial speed
    θ = initial angle
    s = range
    h = height above ground (also works below)
    g = gravitational acceleration (positive)

    let a = 0.5 * g * s2
    let b = cos2θ * (s * tanθ + h)

    v = Math.sqrt(a / b)

    and it works!!!!!
    thanks for all your hard work guys, it paid off this time
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