The body is thrown at an angle to the horizon in such a way that the maximum lift was equal to the flight range

The body is thrown at an angle to the horizon in such a way that the maximum lift was equal to the flight range. At what angle were the bodies thrown?

Since the flight range of a given body after a throw, according to the condition, is equal to the maximum lifting height, then the equality will be true: S = V0 ^ 2 * sin2α / g = V0 ^ 2 * sin2α / 2g = hmax, whence sin2α = sin2α / 2 and 2 * sin2α = sin2α.

Let’s perform trigonometric transformations: 2 * 2 * sinα * cosα = sin2α.

2 * 2 * cosα = sinα.

4 = sinα / cosα = tgα.

α = arctg4.

α = 75.984º.

Answer: The body was thrown at an angle of 75.984º to the horizon.