Question

Снаряд массой 100 кг летит со скоростью 100 м/с горизонтально, попадает в неподвижную тележку массой 400 кг и застревает в ней. С какой скоростью будет двигаться тележка после взаимодействия?

Answer 1

Дано:
m=100 кг
M=400 кг
v1=100 м/с
v-?
Решение:
По закону сохранения импульса: m*v1=v*(M+m) -> v=m*v1/(M+m)=100*100/(100+400)=20 (м/с)
Ответ: 20 м/с.

Answer 2

Calculation of the Final Velocity of the Cart

To determine the final velocity of the cart after the interaction with the projectile, we can use the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.

The momentum of an object is calculated by multiplying its mass by its velocity. In this case, we have a projectile with a mass of 100 kg and a velocity of 100 m/s, and a cart with a mass of 400 kg.

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

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

Momentum of the projectile before the interaction = 100 kg × 100 m/s

To find the total momentum before the interaction, we need to consider that the cart is initially at rest. Therefore, its momentum is zero.

Total momentum before the interaction = momentum of the projectile before the interaction + momentum of the cart before the interaction

Total momentum before the interaction = (100 kg × 100 m/s) + 0

After the interaction, the projectile becomes embedded in the cart, and they move together. Let's assume the final velocity of the cart and the projectile after the interaction is v.

The total momentum after the interaction is given by:

Total momentum after the interaction = (mass of the projectile + mass of the cart) × final velocity

Total momentum after the interaction = (100 kg + 400 kg) × v

According to the principle of conservation of momentum, the total momentum before the interaction is equal to the total momentum after the interaction. Therefore, we can equate the two expressions:

(100 kg × 100 m/s) + 0 = (100 kg + 400 kg) × v

Simplifying the equation, we can solve for v:

10000 kg·m/s = 500 kg × v

v = 10000 kg·m/s / 500 kg

v = 20 m/s

Answer:

After the interaction, the cart will move with a velocity of 20 m/s.