which has a nontrivial solution at 2 θ θ = π π / 2 = 90 ∘ ∘ , or θ θ = 45 ∘ ∘ . The maximum range is then R max = v 2 / g . At this angle sin ⁡ ⁡ ( π π / 2 ) = 1 , so the maximum height obtained is v 2 4 g .