Projectile height formula based on distance?

  • Thread starter Winums2
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If a projectile shot from the ground were shot at a target located at a specified height above the ground, and would hit the target, is there a known formula to find the projectile’s height on its trajectory a specified distance (measured along the flat ground) from the target’s base or from the projectile’s launch point (which is on the ground)? I’m hoping for something based on the distance along the ground rather than on time. I have some rough numbers to use for drag and for lift and numbers for angle and velocity. Seems to me the drag and lift would prevent the trajectory from being the same shape on both sides of the trajectory’s highest point. The entire trajectory would occur over a flat surface.
 

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  • #2
RUber
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So you know trajectory, initial velocity, lift and drag, so you should be able to find h(t) and d(t) where h = height and d = distance. Using these two functions, you can hold t fixed and find t = f(d). Then plug f(d) back into your equation for h(t), giving h(f(d)).
It might get complicated in the algebra, but should not be too hard.
 
  • #3
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Thanks. I'll try to give that a try.
 

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