How will the flight range of a body thrown at an angle to the horizon change

How will the flight range of a body thrown at an angle to the horizon change if, without changing the throwing angle, the initial speed is doubled?

Given:

y1 = y2 = y – the throwing angle of some body has not changed;

v2 = 2 * v1 – the initial speed of the body was doubled.

It is required to determine L2 / L1 – how the flight range of the body will change.

The flight range of the body in the first case will be equal to:

L1 = v1 ^ 2 * sin (2 * y1) / g = v1 ^ 2 * sin (2 * y) / g, where g is the acceleration of gravity.

The flight range of the body in the second case will be equal to:

L2 = v2 ^ 2 * sin (2 * y2) / g = v2 ^ 2 * sin (2 * y) / g.

Then:

L2 / L1 = (v2 ^ 2 * sin (2 * y) / g) / (v1 ^ 2 * sin (2 * y) / g) = v2 ^ 2 / v1 ^ 2 = (2 * v1) ^ 2 / v1 ^ 2 = 4 * v1 ^ 2 / v1 ^ 2 = 4, that is, it will increase by 4 times.

Answer: with an increase in the initial speed by 2 times, the flight range of the body will increase by 4 times.