From a rifle weighing 5 kg, suspended horizontally on cords, a bullet weighing 7 g takes off at a speed of 520 m / s

From a rifle weighing 5 kg, suspended horizontally on cords, a bullet weighing 7 g takes off at a speed of 520 m / s. To what height does the rifle rise from its initial position after firing?

Given:

m1 = 5 kilograms is the mass of the rifle;

m2 = 7 grams = 0.007 kilograms – bullet weight;

v2 = 520 m / s – bullet speed;

g = 10 m / s2 – acceleration of gravity.

It is required to determine to what height h (meter) the rifle will rise after firing.

Let’s find the rifle speed after firing (according to the law of conservation of momentum):

v1 = m2 * v2 / m1 = 0.007 * 520/5 = 3.64 / 5 = 0.728 m / s.

Then, according to the law of conservation of energy:

m1 * g * h = m1 * v1 ^ 2/2;

g * h = v1 ^ 2/2;

h = v1 ^ 2 / (2 * g) = 0.7282 / (2 * 10) = 0.53/20 = 0.026 meters = 2.6 centimeters.

Answer: The rifle will rise to a height of 2.6 centimeters.