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Projectile motion. Relationship between R and theta

  1. Nov 2, 2008 #1
    As a part of a lab, we were asked to find the theoretical relationship between R (the range of the projectile) and theta (the launch-angle). There is no recorded value for time.

    equations given are:

    R(θ)=x=d/dt v0x = v0xt-->R(θ)=v0xt v0x=v0cosθ

    z= d/dt(v0z-gt)+z0=v0zt-1/2(gt^2)+z0 v0z=v0sinθ

    anything with a 0x or 0z after means initial in that direction. I am unsure how to make those subscript on the forum

    I have the equation simplified to

    R(θ)=(v0cosθ)*(- v0sinθ±((v0sinθ)^2+2g(z-z0))^1/2))/g

    but the presence of z-z0 is bothersome.... how can I reasonably cancel it out?
  2. jcsd
  3. Nov 2, 2008 #2
    sorry. Simpler way to state the given equations


  4. Nov 2, 2008 #3
    solved for t

    t=(-v0sinθ±( (v0sinθ)^2+2gz)^1/2)/g

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