The body falls from a certain height and travels the last 196 meters in 4 seconds.

The body falls from a certain height and travels the last 196 meters in 4 seconds. From what height and how long did this body fall?

Data: h1 (length of the last part of the path when falling) = 196 m; t1 (duration of the fall from the height h1) = 4 s.

Constants: g (acceleration due to gravity) ≈ 9.8 m / s2.

1) Initial speed: h1 = V1 * t1 + g * t1 ^ 2/2, whence V1 = (h1 – g * t1 ^ 2/2) / t1 = (196 – 10 * 4 ^ 2/2) / 4 = 29 m / s.

2) Total fall time: t = t0 + t1 = V1 / g + t1 = 29 / 9.8 + 4 ≈ 7 s.

3) Initial height: h0 = g * t ^ 2/2 = 9.8 * 7 ^ 2/2 ≈ 240 m.

Answer: The body started falling from a height of 240 m and its fall lasted 7 seconds.