Question

Человек массой 100кг прыгает с горизонтально направленной скоростью 6 м\с в неподвижную лодку берега. Масса лодки 200кг. с какой скоростью начинает двигаться лодка с человеком?

Answer 1

Дано:

m₁=100 кг

m₂=200 кг

V₁=6 м/с

V₂=0 м/с

Найти: V 

Решение:

По закону сохранения импульса в векторном виде:

m₁*V₁+m₂*V₂=(m₁+m₂)*V -----> отсюда выразим V:

V=(m₁*V₁+m₂*V₂)/(m₁+m₂)=(100*6+6*0)/(100+200)=600/300=2 м/с.

Ответ: V=2 м/с.

 

Answer 2

Calculation of the Boat's Velocity

To calculate the velocity at which the boat with the person starts moving, we can use the principle of conservation of momentum. According to this principle, the total momentum before the jump is equal to the total momentum after the jump.

The momentum of an object is given by the product of its mass and velocity. Let's denote the mass of the person as m1 (100 kg) and the mass of the boat as m2 (200 kg). The initial velocity of the person is v1 (6 m/s), and we need to find the final velocity of the boat with the person, denoted as v2.

Using the conservation of momentum equation, we have:

m1 * v1 + m2 * 0 = (m1 + m2) * v2

Since the boat is initially at rest, its initial velocity is 0. Rearranging the equation, we can solve for v2:

v2 = (m1 * v1) / (m1 + m2)

Substituting the given values:

v2 = (100 kg * 6 m/s) / (100 kg + 200 kg)

Calculating the result:

v2 = 2 m/s

Therefore, the boat with the person starts moving with a velocity of 2 m/s.

Please note that the above calculation assumes an idealized scenario without considering factors such as friction or air resistance.