At what maximum speed does a 20 g ball fly out of a children’s pistol if the maximum spring compression

At what maximum speed does a 20 g ball fly out of a children’s pistol if the maximum spring compression is 4 cm? Spring rate 200N / m.

Problem data: m (ball mass) = 20 g (0.02 kg); Δx (maximum compression of the children’s pistol spring) = 4 cm (0.04 m); k (spring rate) = 200 N / m.

The maximum speed at which the ball will fly out of the children’s pistol is determined from the equality: Ek = En and m * V ^ 2/2 = k * Δx ^ 2/2, whence V = √ (k * Δx ^ 2 / m).

Calculation: V = √ (200 * 0.04 ^ 2 / 0.02) = 4 m / s.

Answer: The ball can fly out of a children’s pistol with a maximum speed of 4 m / s.