The body falls from a height of H = 400 m with zero initial velocity. Ignoring the air resistance

| February 19, 2021 | education

The body falls from a height of H = 400 m with zero initial velocity. Ignoring the air resistance, determine how long it will take for the body to travel: 1) the first 100 m of the path; 2) the last 100 meters of the way.

Given: h (total fall height) = 400 m; Vн (initial falling speed) = 0 m / s.

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

1) Fall time on the first 100 meters of the path (h1 = 100 m): h1 = g * t12 / 2; t1 = √ (2h1 / g) = √ (2 * 100/10) = 4.472 s.

2) All fall time: t = √ (2h / g) = √ (2 * 400/10) = 8.944 s.

3) The duration of the fall to the remaining 100 meters of the path: t3 = √ (2 * (h – h2) / g) = √ (2 * (400 – 100) / 10) = 7.746 s.

4) Fall time on the last 100 meters: t2 = t – t3 = 8.944 – 7.746 = 1.198 s.

Answer: The body will spend 4.472 s and 1.198 s, respectively, to pass the first and last 100 meters of the path.



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