Question

Снаряд массой 15 кг,летящий горизонтально со скоростью 200м/с,попадает в неподвижную платформу с песком массой 2т и застревает в песке .С какой скоростью стала двигаться платформа? 20баллов

Answer 1

По закону сохранения импульса: m1v1+m2v2= v(m1+m2), т.к. платформа была неподвижна, получаем m1v1= v(m1+m2), выразим v =m1v1/(m1+m2),
v = 15*200/2000+15 = 1,49 м/с = 1,5 м/с

Answer 2

Calculation of Final Velocity of the Platform

To determine the final velocity of the platform after the projectile hits it, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is calculated by multiplying its mass by its velocity. In this case, the momentum of the projectile before the collision is given by:

Momentum of the projectile before collision = mass of the projectile × velocity of the projectile

Given that the mass of the projectile is 15 kg and its velocity is 200 m/s, we can calculate its momentum:

Momentum of the projectile before collision = 15 kg × 200 m/s

Now, let's consider the platform with sand. The platform is initially at rest, so its momentum before the collision is zero.

After the collision, the projectile becomes embedded in the sand on the platform. This means that the combined mass of the projectile and the sand is now the mass of the platform with the sand.

Given that the mass of the platform with the sand is 2 tons (or 2000 kg), we can calculate the final velocity of the platform using the conservation of momentum principle:

Momentum of the projectile before collision = Momentum of the platform after collision

15 kg × 200 m/s = (mass of the platform with sand) × (final velocity of the platform)

Now we can solve for the final velocity of the platform:

Final velocity of the platform = (15 kg × 200 m/s) / (mass of the platform with sand)

Substituting the given mass of the platform with sand (2000 kg) into the equation, we can calculate the final velocity of the platform.

Please note that the equation assumes an idealized scenario with no external forces acting on the system.

Let's calculate the final velocity of the platform using the given values:

Final velocity of the platform = (15 kg × 200 m/s) / 2000 kg

Calculating the above expression, we find that the final velocity of the platform is 1.5 m/s.

Therefore, the platform starts moving with a velocity of 1.5 m/s after the projectile hits it and gets embedded in the sand.

- Source: '2' - Source: 'Full text of "Kvant Journal"'