The spring gun shoots the ball vertically upwards to a height of 60 cm if the spring is compressed by 2 cm

The spring gun shoots the ball vertically upwards to a height of 60 cm if the spring is compressed by 2 cm. To what height does the ball rise if the spring is compressed by 5 cm?

Problem data: h1 (the first height of the ball rise) = 60 cm = 0.6 m; Δx1 (first compression) = 2 cm = 0.02 m; Δx ^ 2 (considered compression) = 5 cm = 0.05 m.

1) We transform the equality obtained from the law of conservation of energy: k * Δx2 / 2 = m * g * h, whence k = 2 * m * g * h / Δx ^ 2.

2) Determine the lift of the ball when the spring of the gun is compressed by 5 cm: 2 * m * g * h1 / Δx1 ^ 2 = 2 * m * g * h2 / Δx2 ^ 2, whence h2 = h1 * Δx2 ^ 2 / Δx1 ^ 2 = 0.6 * 0.05 ^ 2 / 0.02 ^ 2 = 3.75 m.

Answer: The ball will be able to rise to a height of 3.75 m.