The bullet strikes at a speed of 400 m / s at the center of the ball suspended by a long string

The bullet strikes at a speed of 400 m / s at the center of the ball suspended by a long string, and bounces off it after an elastic collision. To what height does the center of the ball rise if the mass of the bullet is 15 g, and the mass of the ball is 10 kg?

Data: Vp (bullet speed before hitting the center of the ball) = 400 m / s; mp (bullet weight) = 15 g = 0.015 kg; msh (ball weight) = 10 kg.

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

To determine the height of the rise of the center of the ball, we use the equality (work to reduce the kinetic energy of the bullet went to increase the potential energy of the ball): mp * Vp ^ 2/2 = mw * g * h, whence h = mp * Vp2 / (2 * mw * g).

Calculation: h = 0.015 * 400 ^ 2 / (2 * 10 * 10) = 12 m.

Answer: The center of the ball will rise 12 m.