Given Angle, Initial Velocity, and Acceleration due to Gravity, plot parabolic trajectory for every x?Given any Angle -&gt; 0-90Given any Initial Velocity -&gt; 1-100Given Acceleration due to Gravity -&gt; 9.8Plot every x,y coordinate (the parabolic trajectory) with cartesian coordinates and screen pixels (not time)This should only be one equation as far as I can tell, a "y=" type equation, telling you the height in y coordinates based on the current x coordinate which is increasing by 1 as you plot across a computer screen.I've come up with an equation that works for the angle 45, but doesn't seem to be entirely accurate for any other angle, I suspect it has something to do with the angle 45 having 1 solution and every other angle having 2 solutions (two different initial velocities land on the same spot), but I'm stumped beyond that. y = y 0 − ( x − x 0 ) ⋅ tan ⁡ 1 2 ⋅ 9.8 v 0 2 ⋅ x − x 0 2 cos ⁡ θ 2

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Given Angle, Initial Velocity, and Acceleration due to Gravity, plot parabolic trajectory for every   x?Given any Angle -&amp;gt; 0-90Given any Initial Velocity -&amp;gt; 1-100Given Acceleration due to Gravity -&amp;gt; 9.8Plot every x,y coordinate (the parabolic trajectory) with cartesian coordinates and screen pixels (not time)This should only be one equation as far as I can tell, a &quot;y=&quot; type equation, telling you the height in y coordinates based on the current x coordinate which is increasing by 1 as you plot across a computer screen.I&#039;ve come up with an equation that works for the angle 45, but doesn&#039;t seem to be entirely accurate for any other angle, I suspect it has something to do with the angle 45 having 1 solution and every other angle having 2 solutions (two different initial velocities land on the same spot), but I&#039;m stumped beyond that.  y  =      y    0    −  (  x  −      x    0    )  ⋅  tan  ⁡                    1        2            ⋅              9.8                  v          0          2                    ⋅      x      −              x        0        2                    cos      ⁡              θ        2

Timothy Mcclure · Accepted Answer

Starting as Pieter Geerkens, the equations of motion in 2-D a parabolic system:  x  (  t  )  =      x    0    +      v    x    t  =      x    0    +      v    0    cos  ⁡  (  α  )  tand int the   y axis:  y  (  t  )  =      y    0    +      v    0    sin  ⁡  (  α  )  t  +      1    2    g      t    2  where   g  ∼  −  9.8 is the gravitational acceleration.Solvinf for t in the first equation as Pieter did:  t  (  x  )  =            x      −              x        0                            v        0            cos      ⁡      (      α      )      and then substituitint   t  (  x  ) in   y  (  t  )  y  (  x  )  =  y  (  t  (  x  )  )  =      y    0    +      v    0    sin  ⁡  (  α  )  ⋅            x      −              x        0                            v        0            cos      ⁡      (      α      )        +      1    2    g            (                        x          −                      x            0                                                v            0                    cos          ⁡          (          α          )                    )        2  Then if your math is not good enoguh to do this algebraic manipulations you should study some of math to keep going. It&#039;s worth it.

junoonib89p4 · Accepted Answer

First consider parametric equations for x and y as a function of t.Now, for each   x-value solve for   t  =  (  x  −      x    0    )      /    (      v    0    ⋅  cos  ⁡  (  θ    )  )Then solve for the corresponding   y  =      y    0    +      v    0    ⋅  sin  ⁡  (  θ    )  ⋅  t  −  4.9  ⋅      t    2

Given Angle, Initial Velocity, and Acceleration due to Gravity, plot parabolic trajectory for every

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