Question

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

Answer 1

По ЗСИ
30•300+2000•2=(30+2000)v
9000+4000=2030v
13000=2030v
v=13000/2030=6,4 (м/с)

Answer 2

Problem Analysis

We are given a scenario where 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 2 tons (2000 kg), and gets stuck in the sand. We need to determine the velocity of the cart after the projectile hits it, given that the cart was initially moving with a velocity of 2 m/s in the direction of the projectile's motion.

Solution

To solve this problem, we can apply 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. Mathematically, momentum (p) is defined as:

p = m * v

where p is the momentum, m is the mass, and v is the velocity.

Before the collision, the momentum of the projectile is given by:

p_projectile = m_projectile * v_projectile

After the collision, the projectile gets stuck in the cart, so the momentum of the cart and the projectile together is equal to the momentum of the cart after the collision. The momentum of the cart before the collision is given by:

p_cart = m_cart * v_cart

Using the principle of conservation of momentum, we can equate the total momentum before the collision to the total momentum after the collision:

p_projectile + p_cart = p_cart_after_collision

Substituting the values given in the problem, we have:

(m_projectile * v_projectile) + (m_cart * v_cart) = (m_cart_after_collision * v_cart_after_collision)

We are given the mass of the projectile (30 kg), the velocity of the projectile (300 m/s), the mass of the cart (2000 kg), and the initial velocity of the cart (2 m/s). We need to solve for the final velocity of the cart (v_cart_after_collision).

Calculation

Let's substitute the given values into the equation and solve for v_cart_after_collision:

(30 kg * 300 m/s) + (2000 kg * 2 m/s) = (m_cart_after_collision * v_cart_after_collision)

Simplifying the equation:

9000 kg*m/s + 4000 kg*m/s = (m_cart_after_collision * v_cart_after_collision)

13000 kg*m/s = (m_cart_after_collision * v_cart_after_collision)

To find the final velocity of the cart (v_cart_after_collision), we need to know the mass of the cart after the collision (m_cart_after_collision). However, this information is not provided in the problem statement. Without the mass of the cart after the collision, we cannot determine the final velocity of the cart.

Therefore, we cannot calculate the final velocity of the cart without additional information.

Conclusion

Based on the information provided in the problem statement, we cannot determine the final velocity of the cart after the projectile hits it. We need to know the mass of the cart after the collision to calculate the final velocity.