A bullet with a mass of m = 10 g, flying horizontally at a speed of v = 500 m / s, hits a ballistic pendulum with a length

A bullet with a mass of m = 10 g, flying horizontally at a speed of v = 500 m / s, hits a ballistic pendulum with a length of L – 1 m and a mass of M = 5 kg and gets stuck in it. Determine the angle of deflection of the pendulum.

According to the law of conservation of momentum: mV = V` (m + M), hence V` = mV / (m + M), and will be approximately equal to 1m / s. According to the law of conservation of energy: (m + M) V` ^ 2/2 = (m + M) gh, hence h = V` ^ 2 / 2g, and we get: h = 0.05m Hence, the cosine of the deflection angle is: cos a = (L – h) / L = 0.95, => a = 18 °