The ball was thrown in a horizontal direction at a speed v0. At the same time, the same ball was thrown

The ball was thrown in a horizontal direction at a speed v0. At the same time, the same ball was thrown from the same height without initial velocity. Which of the balls reaches the ground first and why.

The total time of movement of both balls along their own trajectories can be calculated by the formula:

ttotal = (√ (v² * sin² a + 2 * g * h) + v * sin a) / g.

1. The ball moves in the horizontal direction (v, h, sin 0 = 0), we have:

t1 = √ (2 * g * h) / g.

2. The ball moves in the vertical direction (falls down from the same height, v = 0, h, sin 0 = 0), therefore:

t2 = √ (2 * g * h) / g.

Thus, t1 = t2, i.e. both balls will reach the surface of the earth in the same amount of time.