Question

A bullet with mass 120g hits a ballistic pendulum with mass 30kg and lodges in it. When the bullet hits the pendulum it swings up reaching the height of 0.25m. Neglecting air resistance, calculate the speed of the bullet. 

Answer 1

Apply the law of kinetic energy: the bullet and pendulum's kinetic energy converts into potential energy of the box and the bullet. Find the velocity $v$ of the bob and the bullet:

$$\frac12(M+m)v^2=(M+m)gh,\\\space\\ v=\sqrt{2gh}.$$

Momentum conservation: momentum of the bullet converts into momentum of the bullet and the bob. Find the velocity of the bullet $u$:

$$mu=(M+m)v,\\\space\\ u=\frac{M+m}{m}v=\frac{M+m}{m}\sqrt{2gh}=556\text{ m/s}.$$