A stone fell from the tower with zero initial velocity. In the last second, he flew 0.75 of

A stone fell from the tower with zero initial velocity. In the last second, he flew 0.75 of the entire path. Determine the time of its fall. Air resistance is negligible.

Ignoring the force of air resistance, the movement of the stone along the vertical is uniformly accelerated, with the acceleration of gravity g = 9.8 m / s2.

Vertical motion equation:

H = gt² / 2,

where H is the initial height, m; t – fall time, s.

The fall of a stone in time (t −1):

h = g (t − 1) ² / 2.

According to the condition of the problem: H – h = 0.75 H,

whence: 0.25 H = h, → 0.125 gt² = gt² / 2 – gt + g / 2; → 0.375 gt ² – gt + 0.5g = 0;

3.675 t ² – 9.8 t + 4.9 = 0; D = 24.01;

whence t = (9.8 + 24.010.5) / (2 × 3.675) = 2.0 s.