Question

1.Две тележки движутся навстречу друг другу со скоростью 4 м/с каждая. После столкновения вторая тележка получила скорость равную 6 м/с,в направлении движения первой тележки ,а первая остановилась. Рассчитайте массу первой тележки,если масса второй равна 2 кг 2.Охотник стреляет с лёгкой надувной лодки,находящейся в покое. Какую скорость приобретает лодка в момент выстрела,если масса охотника вместе с лодкой равна 120 кг,масса дроби равна 35 г, начальная скорость дроби равна 320 м/с? Ствол ружья во время выстрела направлен под углом 60 градусов к горизонту.  

Answer 1

Calculation of the mass of the first cart:

To calculate the mass of the first cart, 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. Let's denote the mass of the first cart as m1 and its initial velocity as v1. The mass of the second cart is given as 2 kg, and its initial velocity is also 4 m/s.

Before the collision, the total momentum is given by:

Total momentum before collision = (m1 * v1) + (2 kg * 4 m/s)

After the collision, the first cart comes to a stop, so its final velocity is 0 m/s. The second cart acquires a velocity of 6 m/s in the direction of the first cart's initial motion. Therefore, the total momentum after the collision is:

Total momentum after collision = (m1 * 0 m/s) + (2 kg * 6 m/s)

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

(m1 * v1) + (2 kg * 4 m/s) = (m1 * 0 m/s) + (2 kg * 6 m/s)

Simplifying the equation, we get:

m1 * v1 + 8 kg m/s = 12 kg m/s

Since the first cart comes to a stop after the collision, its final velocity is 0 m/s. Therefore, the equation becomes:

m1 * 0 m/s + 8 kg m/s = 12 kg m/s

Simplifying further, we find:

8 kg m/s = 12 kg m/s

Dividing both sides of the equation by 8 kg m/s, we get:

m1 = 12 kg m/s / 8 kg m/s = 1.5 kg

Therefore, the mass of the first cart is 1.5 kg.

Calculation of the velocity acquired by the boat:

To calculate the velocity acquired by the boat after the shot, we can use the principle of conservation of momentum again. The total momentum before the shot is equal to the total momentum after the shot.

Let's denote the mass of the boat and the hunter together as m2, and the initial velocity of the boat as v2. The mass of the shot is given as 35 g (0.035 kg), and its initial velocity is 320 m/s. The initial velocity of the boat is 0 m/s since it is at rest.

Before the shot, the total momentum is given by:

Total momentum before shot = (m2 * 0 m/s) + (0.035 kg * 320 m/s)

After the shot, the boat acquires a velocity, which we'll denote as v3. The total momentum after the shot is:

Total momentum after shot = (m2 * v3) + (0.035 kg * v3)

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

(m2 * 0 m/s) + (0.035 kg * 320 m/s) = (m2 * v3) + (0.035 kg * v3)

Simplifying the equation, we get:

0 kg m/s + 11.2 kg m/s = (m2 + 0.035 kg) * v3

Since the boat is at rest initially, its initial velocity is 0 m/s. Therefore, the equation becomes:

0 kg m/s + 11.2 kg m/s = (m2 + 0.035 kg) * v3

Simplifying further, we find:

11.2 kg m/s = (m2 + 0.035 kg) * v3

Dividing both sides of the equation by (m2 + 0.035 kg), we get:

v3 = 11.2 kg m/s / (m2 + 0.035 kg)

Given that the mass of the hunter and the boat together is 120 kg, we can substitute this value into the equation:

v3 = 11.2 kg m/s / (120 kg + 0.035 kg) = 11.2 kg m/s / 120.035 kg

Calculating the value, we find:

v3 ≈ 0.093 m/s

Therefore, the boat acquires a velocity of approximately 0.093 m/s after the shot.

Note: The angle at which the gun barrel is directed does not affect the calculation of the boat's velocity, as the principle of conservation of momentum only considers the total momentum before and after the shot.