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v0y = v0 sinα
∆t1=v0y/g = v0/g sinα
∆H=g/2 ∆t1² = g/2 (v0y/g)² = v0²/2g sin²α
Hmax=H+∆H = H +v0²/2g sin²α
Hmax = g/2 ∆t2²
∆t2 = √(2Hmax/g) = √(2H/g + v0²/g² sin²α)
Δt=∆t1+ ∆t2 = v0/g sinα + √(2H/g + v0²/g² sin²α)
L=∆t∙v0x = (v0/g sinα + √(2H/g + v0²/g² sin²α)) v0 cosα = v0²/g sinα cosα + v0 cosα√(2H/g + v0²/g² sin²α)
v1x=v0x = v0 cosα
v1y=g∙∆t2 = g√(2H/g + v0²/g² sin²α)
v1=√(v1x²+v1y²)=√(v0² cos²α + g²(2H/g + v0²/g² sin²α)) = √(v0² cos²α + v0² sin²α + 2gH) = √(v0²+2gH)
β=arccos(v1x/v1) = arccos (v0 cosα/√(v0²+2gH))