Question

Снаряд массой 30 кг, летящий горизонтально со скоростью 300 м/с, попадает в вагонетку с песком массой 1,2 т и застревает в песке.С какой скоростью будет двигаться вагонетка, если до попадания снаряда она двигалась со скоростью 2 м/с в направлении движения снаряда?

Answer 1

M и M - массы снаряда и тележки соответственно, v и u - их скорости

напишем закон сохранения импульса в проекции на ось, сонаправленную с векторами v и u, учитывая, что удар абсолютно неупругий:

mv + Mu = (m + M) U, где U - скорость снаряда и тележки после соударения

U = (mv + Mu)/(m + M)

U = (30*300+1200*2)/1230 ≈ 9.27 м/c

Answer 2

Problem Analysis

We are given the following information: - A projectile with a mass of 30 kg is flying horizontally with a velocity of 300 m/s. - The projectile hits a cart filled with sand, which has a mass of 1.2 tons (or 1200 kg). - The cart was initially moving with a velocity of 2 m/s in the same direction as the projectile.

We need to determine the velocity of the cart after the projectile hits it.

Solution

To solve this problem, 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 given by the product of its mass and velocity: momentum = mass × velocity.

Before the collision, the momentum of the projectile is momentum_projectile = mass_projectile × velocity_projectile.

The momentum of the cart before the collision is momentum_cart = mass_cart × velocity_cart.

After the collision, the projectile becomes embedded in the cart, so the combined mass of the cart and the projectile is mass_combined = mass_cart + mass_projectile.

The momentum of the combined system after the collision is momentum_combined = mass_combined × velocity_combined.

According to the conservation of momentum principle, we have:

momentum_projectile + momentum_cart = momentum_combined

Substituting the formulas for momentum, we get:

mass_projectile × velocity_projectile + mass_cart × velocity_cart = mass_combined × velocity_combined

We can rearrange this equation to solve for the velocity of the cart after the collision:

velocity_combined = (mass_projectile × velocity_projectile + mass_cart × velocity_cart) / mass_combined

Now we can substitute the given values into this equation to find the velocity of the cart after the collision.

Calculation

Given: - mass_projectile = 30 kg - velocity_projectile = 300 m/s - mass_cart = 1200 kg - velocity_cart = 2 m/s

Substituting these values into the equation, we get:

velocity_combined = (30 kg × 300 m/s + 1200 kg × 2 m/s) / (30 kg + 1200 kg)

Simplifying the equation, we have:

velocity_combined = (9000 kg·m/s + 2400 kg·m/s) / 1230 kg

velocity_combined = 11400 kg·m/s / 1230 kg

velocity_combined ≈ 9.27 m/s

Therefore, the velocity of the cart after the collision is approximately 9.27 m/s.

Answer

The velocity of the cart after the projectile hits it will be approximately 9.27 m/s.