Question

Граната летящая со скоростью 15м/с разорвалась на два осколка массами 6 и 14 кг. Скорость большего возросла до 24 м/с по направлению движения. Найти скорость и направление движения меньшего осколка, если осколки движутся вдоль первоначального движения снаряда.

Answer 1

В данной задаче сохраняется импульс системы

начальный импульс 20 кг * 15 м/с
конечный импульс    14 кг * 24 м/с +6 кг * u
u - скорость 2 осколка

300 = 336 +6u

u = -6 м/с - движется в направлении, обратном первоначальному 

Answer 2

Problem Analysis

We are given that a grenade traveling at a speed of 15 m/s exploded into two fragments with masses of 6 kg and 14 kg. The speed of the larger fragment increased to 24 m/s in the direction of the original motion. We need to find the speed and direction of motion of the smaller fragment.

Solution

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the explosion is equal to the total momentum after the explosion.

Let's denote the initial velocity of the grenade as v and the final velocities of the fragments as v1 and v2 for the smaller and larger fragments, respectively. The masses of the fragments are m1 = 6 kg and m2 = 14 kg.

The total momentum before the explosion is given by: mv = m1v1 + m2v2

We are given that v = 15 m/s and v2 = 24 m/s. Substituting these values into the equation, we can solve for v1.

Calculation

mv = m1v1 + m2v2 15 * (6 + 14) = 6 * v1 + 14 * 24 15 * 20 = 6 * v1 + 14 * 24 300 = 6 * v1 + 336 6 * v1 = 300 - 336 6 * v1 = -36 v1 = -36 / 6 v1 = -6 m/s

The negative sign indicates that the smaller fragment is moving in the opposite direction of the original motion of the grenade.

Answer

The speed and direction of motion of the smaller fragment are 6 m/s in the opposite direction of the original motion of the grenade.