# A bullet weighing 15 g, flying horizontally, hits a ballistic pendulum with a length of 1 m and a mass

**A bullet weighing 15 g, flying horizontally, hits a ballistic pendulum with a length of 1 m and a mass of 1.5 kg and gets stuck in it. As a result, the pendulum deflected by an angle of 300. Determine the speed of the bullet**

mp = 15 g = 0.015 kg.

L = 1 m.

g = 10 m / s2.

mm = 1.5 kg.

∠α = 30 °.

Vп -?

Let us write down the law of conservation of momentum: mp * Vp = (mp + mm) * V, where V is the speed of the bullet from the pendulums after hitting.

Vp = (mp + mm) * V / mp.

We find the speed of a bullet with a pendulum, according to the law of conservation of total mechanical energy:

(mp + mm) * V2 / 2 = (mp + mm) * g * h, where h is the height to which the pendulum with the bullet rose.

V2 / 2 = g * h.

h = L – L * cosα = L * (1 – cosα).

V = √ (2 * g * L * (1 – cosα)).

V = √ (2 * 10 m / s2 * 1 m * (1 – cos30 °)) = 1.6 m / s

Vp = (0.015 kg + 1.5 kg) * 1.6 m / s / 0.015 kg = 161.6 m / s.

Answer: the bullet was moving at a speed of Vp = 161.6 m / s.