Question

Снаряд массой 20кг, летевший горизонтально, попадает в платформу с песком 10кг в 4 степени и застревает в песке. С какой скоростью летел снаряд, если платформа начала двигаться со скоростью 1 м/с

Answer 1

По закону сохранения импульса (учитывая, что после застревания снаряда, вагон со снарядом движутся с одинаковой скоростью) имеем:
Mв·Vв+Мс·Vс = (Мв+Мс)·V
откуда
V = (Mв·Vв+Мс·Vс) / (Мв+Мс)
Подставляя заданные значения (все выражено в кг и м/сек, Vc отрицательна из-за встречного движения)
(10000·10–100·500) / 10100 = 500/101 = 4.95 м/сек
Т.е. вагон замедлится более чем в два раза...
Если ищешь скорость.

Answer 2

Calculation of Projectile Velocity

To determine the velocity of the projectile before it hit the sand platform, we can use the principle of conservation of momentum. The initial momentum of the system (projectile + sand platform) is equal to the final momentum of the system.

Let's denote the mass of the projectile as m1 (20 kg) and the mass of the sand platform as m2 (10 kg). The initial velocity of the projectile is v1 (unknown), and the velocity of the sand platform is v2 (1 m/s).

According to the conservation of momentum, the equation can be written as:

m1 * v1 = (m1 + m2) * vf

Where vf is the final velocity of the system after the projectile gets embedded in the sand platform.

To solve for v1, we need to find vf first. We can use the equation for the conservation of kinetic energy to find vf:

0.5 * (m1 + m2) * vf^2 = 0.5 * m1 * v1^2

Simplifying the equation, we have:

(m1 + m2) * vf^2 = m1 * v1^2

Substituting the given values, we have:

(20 + 10) * vf^2 = 20 * v1^2

Simplifying further:

30 * vf^2 = 20 * v1^2

Dividing both sides by 30:

vf^2 = (20/30) * v1^2

Taking the square root of both sides:

vf = sqrt((20/30) * v1^2)

Now, let's substitute the value of vf into the conservation of momentum equation:

m1 * v1 = (m1 + m2) * vf

20 * v1 = (20 + 10) * sqrt((20/30) * v1^2)

Simplifying the equation, we have:

20 * v1 = 30 * sqrt((20/30) * v1^2)

Squaring both sides:

400 * v1^2 = 900 * (20/30) * v1^2

Simplifying further:

400 * v1^2 = 600 * v1^2

Dividing both sides by v1^2 (assuming v1 is not zero):

400 = 600

This equation is not possible to solve, as it leads to a contradiction. Therefore, there is no valid solution for the velocity of the projectile based on the given information.

Please note that the given information may be incomplete or there may be an error in the problem statement. If you have any additional information or clarification, I would be happy to assist you further.