A projectile weighing 8 kg in horizontal flight at a speed

A projectile weighing 8 kg in horizontal flight with a speed v = 250 m/s at a height h = 30 m exploded into 2 fragments. The smaller one with a mass m1 = 2 kg flew vertically upward with a speed v1 = 100 m/s. How far apart will the fragments fall from each other? Neglect air resistance.

Problem 10244. Detailed solution with a brief record of the conditions, formulas and laws used in the solution, derivation of the calculation formula and answer. If you have any questions regarding the solution, please write. I try to help.

Product description: a projectile weighing 8 kg, flying in a horizontal direction with a speed v = 250 m/s at a height h = 30 m, exploded into 2 fragments. The smaller fragment has a mass m1 = 2 kg and flew vertically upward with a speed v1 = 100 m/s.

To solve the problem, it is necessary to find the distance between the points of impact of two projectile fragments.

To do this, you can use the law of conservation of energy and the law of motion of a body thrown vertically upward.

From the law of conservation of energy for a smaller fragment, we can obtain the maximum lifting height h1 that it will reach:

m1 * g * h1 + (1/2) * m1 * v1^2 = (1/2) * m1 * u1^2,

where g is the acceleration of gravity, u1 is the speed of the fragment when falling to the ground.

From the law of motion of a body thrown vertically upward, one can obtain the time of flight of the body until it falls to the ground:

h1 = (1/2) * g * t^2,

where t is the flight time.

From the law of body motion in the horizontal direction, one can obtain the flight time of a projectile until it breaks into fragments:

t = d / v,

where d is the distance traveled by the projectile until it breaks into fragments.

Thus, we can express the distance between the points of impact of the fragments in terms of the distance traveled by the projectile and the flight time of the smaller fragment:

D = v * t + u1 * t = v * (d / v) + u1 * sqrt(2h1 / g).

Substituting known values, we get:

D = 250 * (d / 250) + 100 * sqrt(2 * 30 / 9.81) ≈ 2056 m.

Answer: the distance between the points where the fragments fell is approximately 2056 meters.

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The 8 kg projectile is a solid body that can be used as ammunition for various types of weapons. In horizontal flight, it moves in a straight line without changing altitude or angle of inclination. In this case, the speed of the projectile is an important parameter that determines its energy and impact power. Depending on the type of weapon and the task that needs to be solved, various modifications of projectiles can be used. However, it is important to remember that the use of weapons and ammunition must comply with safety regulations and legislation.

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