The initial velocity of the projectile is 500 m / s. Disregarding air resistance, show at what angle

The initial velocity of the projectile is 500 m / s. Disregarding air resistance, show at what angle to the horizon a shot should be fired to achieve the maximum range and determine the maximum flight range.

So that, neglecting air resistance, it was possible to calculate at what angle to the horizon a shot should be fired to achieve the maximum flight range, consider the projection of the velocity vector (or its coordinates). They will be a pair of numbers Vx = V • cos α; Vy = V • sin α. The flight time can be found t = (2 • Vy): g, then the flight range will be L = t • Vx; L = (2 • V • V • cos α • sin α): g; L = (V • V • sin 2 α): g. This product will have the maximum value if sin 2 α = 1; α = 45º.
Since the initial velocity of the projectile is 500 m / s, the maximum flight range. L = (V • V • 1): g. L ≈ 25510 m. Answer: at an angle α = 45º to the horizon, a shot must be fired to achieve the maximum flight range, the maximum flight range is L ≈ 25510 m.