The body falls freely from a height h without an initial velocity. In the last second it covers

The body falls freely from a height h without an initial velocity. In the last second it covers the distance S = 25 m. Find h.

1. The height that the body flew is found by the formula: h = g * t ^ 2/2, where g is the acceleration of gravity, equal to 10 m / s ^ 2.

2. According to the condition of the problem, an equation was drawn up:

10 * t ^ 2/2 – 10 * (t – 1) ^ 2/2 = 25;

5t ^ 2 – 5 * (t ^ 2 – 2t + 1) = 25;

5t ^ 2 – 5t ^ 2 + 10t – 5 = 25;

10t = 25 + 5;

10t = 30;

t = 30/10;

t = 3;

The flight time was 3 seconds.

3. If t = 3, then h = g * t ^ 2/2 = 10 * 3 * 3/2 = 45 meters.

Answer: the body falls from a height of 45 meters.