Question

На плот массой 100 кг имеющий скорость 1м/ с направленную вдоль берега прыгает человек массой 50 кг со скоростью 1,5 м/ с перпендикулярно берегу. определите скорость плота с прыгнувшим на него человеком.

Answer 1

1)
Находим импульс плота:
p₁ = m₁*V₁ = 100*1 = 100 кг*м/с
2)
Находим импульс человека:
p₂ = m₂*V₂ = 50*1,5 = 75 кг*м/с

3)
Поскольку вектора импульсов перпендикулярны, то по теореме Пифагора суммарный импульс:
p = √ (100² + 75²) = 125 м/с

4)
Теперь общая масса плота с человеком:
m = m₁+m₂ = 100 + 50 = 150 кг
5)
Поскольку
p = m*V
то
V = p/m = 125 / 150 ≈ 0,8 м/с

Answer 2

Problem Analysis

We have a boat with a mass of 100 kg moving with a velocity of 1 m/s along the shore. A person with a mass of 50 kg jumps onto the boat perpendicular to the shore with a velocity of 1.5 m/s. We need to determine the velocity of the boat with the person on it.

Solution

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the person jumps onto the boat is equal to the total momentum after the person jumps onto the boat.

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.

Let's denote the initial velocity of the boat as v1, the final velocity of the boat with the person on it as v2, the mass of the boat as m1, and the mass of the person as m2.

Before the person jumps onto the boat, the total momentum is the sum of the momentum of the boat and the momentum of the person:

Total momentum before = (m1 * v1) + (m2 * 0)

Since the person is initially at rest, their velocity is 0.

After the person jumps onto the boat, the total momentum is the sum of the momentum of the boat with the person on it:

**Total momentum after = (m1 + m2)