A spring-loaded gun shoots the ball vertically upwards to a height of 30 cm when the spring is compressed

| September 16, 2021 | education

A spring-loaded gun shoots the ball vertically upwards to a height of 30 cm when the spring is compressed by 1 cm. What is the initial flight speed of the ball? How high does the ball rise if this spring is compressed by 3 cm.

Data: h1 (first lift height) = 30 cm = 0.3 m; Δx1 (initial compression) = 1 cm = 0.01 m; Δx2 (second compression) = 3 cm = 0.03 m; g (acceleration due to gravity) ≈ 10 m / s2.

1) Speed when lifting 0.3 m: m * g * h = m * V ^ 2/2 and V1 = √ (2 * g * h1) = √ (2 * 10 * 0.1) = 1.41 m / s.

2) We transform the equality obtained from the law of conservation of energy: k * Δх2 / 2 = m * g * h and k / (2 * m * g) = h / Δх2.

3) Lift height: h1 / Δx1 ^ 2 = h2 / Δx2 ^ 2; h2 = h1 * Δx2 ^ 2 / Δx1 ^ 2 = 0.3 * 0.03 ^ 2 / 0.01 ^ 2 = 2.7 m.



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