A stone thrown from the roof of the shed almost vertically upward at a speed of 15

| July 14, 2021 | education

A stone thrown from the roof of the shed almost vertically upward at a speed of 15 m / s fell to the ground after 4 s. Find the height of the roof.

Data: Vb – throw speed (Vb = 15 m / s); t is the total duration of the flight of the stone (t = 4 s).

Const: g – acceleration of gravity (g = 10 m / s2).

Method 1) Equation of motion: S = hcr + Vb * t – 0.5 * g * t ^ 2, from where we express: hcr = S – Vb * t + 0.5 * g * t ^ 2 = 0 – 15 * 4 + 0.5 * 10 * 4 ^ 2 = 20 m.

Method 2) Duration of ascent (time of falling to the roof): tp = Vb / g = 15/10 = 1.5 s.

Falling time from the roof level: tcr = t – 2 * tp = 4 – 2 * 1.5 = 1 s.

Roof height: h = Vb * tcr + 0.5 * g * tcr ^ 2 = 15 * 1 + 0.5 * 10 * 1 ^ 2 = 20 m.

Answer: The height of the roof, according to the calculation, is 20 m.



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