On earth in a vacuum. You throw a platon from a platform height $h$ and want it to land at point $d$ distant. Note, h is absolutely fixed and d is absolutely fixed. It "must land" at point d, no matter what. You throw it with velocity expressed using $Vx$ and $Vy$.
Now,
(Problem AA)
you want the vertex HEIGHT to be at a percentage $H$ >100 of $h$ (say $H=120 \% $).
-- ~~ ~~ OR ~~ ~~ --
(Situation BB)
you want the vertex DISTANCE to be at a percentage $D$ <50 of $d$ (say $D=25 \% $).
NOTE: the two gentlemen below have generously explained that you CANNOT choose BOTH H and D. Thank you very much for this insight and proof!
So! For each of ProblemAA and ProblemBB, how to calculate $Vx$ and $Vy$ ?
If this is possible - thank you!
{Aside: I assume there's only one $Vx$ / $Vy$ solution for a given value in either ProblmeAA or ProblemBB - but could there be two, or more??}