The body falls freely from a height of 540 m. Divide this height into three parts so that each

| September 12, 2021 | education

The body falls freely from a height of 540 m. Divide this height into three parts so that each of them would take the same time to pass.

Task data: h (total fall height) = 540 m.

Constants: g (acceleration due to gravity) ≈ 10 m / s2.

1) The total duration of the fall: h = g * t ^ 2/2, whence t = √ (2h / g) = √ (2 * 540/10) ≈ 10.39 s.

2) Time on each segment: t1 = t / 3 ≈ 3.46 s.

3) The first leg of the path: h1 = g * t1 ^ 2/2 = 10 * 3.46 ^ 2/2 ≈ 60 m.

4) Second leg of the path: h2 = V1 * t1 + g * t1 ^ 2/2 = g * t1 * t1 + g * t1 ^ 2/2 = 3g * t1 ^ 2/2 = 3 * 10 * 3.46 ^ 2/2 ≈ 180 m.

5) Third leg of the path: h3 = V2 * t1 + g * t1 ^ 2/2 = (V1 + g * t1) * t1 + g * t1 ^ 2/2 = (g * t1 + g * t1) * t1 + g * t1 ^ 2/2 = 5g * t1 ^ 2/2 = 5 * 10 * 3.462 / 2 ≈ 300 m.

Check: h = h1 + h2 + h3 = 60 + 180 + 300 = 540 m (correct).



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