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

August 24, 2021 | education

| **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.

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