The body falls freely from the tower at zero initial velocity. It is known that it covered the second half of the journey t = 1s.

The body falls freely from the tower at zero initial velocity. It is known that it covered the second half of the journey t = 1s. Find the height of the tower.

Task data: t2 (duration of the fall in the second half of the trip) = 1 s.

Constants: g (acceleration due to gravity) = 9.81 m / s2.

1) Find the total fall time: h / 2 = g * (t – 1) ^ 2/2 = g * t ^ 2/4.

2 * (t – 1) ^ 2/2 = t ^ 2.

2t ^ 2 – 4t + 2 = t ^ 2.

t ^ 2 – 4t + 2 = 0.

D = 4 ^ 2 – 4 * 1 * 2 = 8.

Fall time (roots): t1 = (- (- 4) + √8) / (2 * 1) = 3.414 s (true) and t2 = (- (- 4) – √8) / (2 * 1) = 0.586 s (incorrect).

2) Tower height: h = g * t ^ 2/2 = 9.81 * 3.4142 / 2 = 57.17 m.

Answer: The tower is 57.17 m high.