What angle to kick a soccer ball to maximize distance traveled? (vector calc)

Question

A soccer ball on the ground is kicked with an initial speed of 44mph at an angle θ above the horizon. What is the angle in radians that will maximize the distance traveled (g=32ft/sec)?

And what will the maximum height and distance traveled be at this angle θ?

Answer 1

x = v₀cosθt, v_x = v₀cosθ; y = v₀sinθt - gt²/2 = 0; t = 2v₀sinθ/g; x = v₀cosθ·2v₀sinθ/g = v₀²sin2θ/g

Because max x = v₀²/g when sin2θ = 1; 2θ = π/2, θ = π/4.