Projectiles in a vaccuum is easy.
The vertical velocity at the apogee is zero.
The maximum distance is achieved with a 45 degree launch angle.
The horizontal speed component and time determine distance.
Flight time is twice the time for the initial vertical velocity to reach zero.
v=u+ft
s=ut+(ft^2)/2
v^2-u^2=2fs
where u is initial velocity
v is final velocity
t is time
s is distance
and f is accelaration
vertical velocity is total initial velocity X Sine of the launch angle.
horizontal velocity ditto except it is Cosine of the launch angle.
PS ladders up a wall use the same sine/cosine rules.
Sine = opposite/hypotenuse (ladder length)
Cosine = adjacent (distance of foot from wall)/hypotenuse