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

Решаем через закон сохраниния импульса.Формула для этой задачи m1v1+m2v2=(m1+m2)u. скорость плота и человека обозначим u.Выразим u из формулы и получим u=(m1v1+m2v2)/(m1+m2).ответ 1.17 м/с

Answer 2

Problem Analysis

We are given a scenario where a person with a mass of 50 kg jumps onto a raft with a mass of 100 kg. The person jumps perpendicular to the shore with a velocity of 1.5 m/s, while the raft is moving parallel to the shore with a velocity of 1 m/s. We need to determine the velocity of the raft with the person on it after the jump.

Solution

To solve this problem, we can apply 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. 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 velocity of the raft after the jump as Vr and the velocity of the person after the jump as Vp. The total momentum before the jump is the sum of the momentum of the raft and the momentum of the person:

Total momentum before jump = (mass of raft * velocity of raft) + (mass of person * velocity of person)

Total momentum after jump = (mass of raft + mass of person) * velocity of raft with person

According to the principle of conservation of momentum, the total momentum before the jump is equal to the total momentum after the jump:

(mass of raft * velocity of raft) + (mass of person * velocity of person) = (mass of raft + mass of person) * velocity of raft with person

We can rearrange this equation to solve for the velocity of the raft with the person:

velocity of raft with person = [(mass of raft * velocity of raft) + (mass of person * velocity of person)] / (mass of raft + mass of person)

Let's substitute the given values into this equation and calculate the velocity of the raft with the person.

Calculation

Given: - Mass of the raft (m1) = 100 kg - Velocity of the raft before the jump (v1) = 1 m/s - Mass of the person (m2) = 50 kg - Velocity of the person before the jump (v2) = 1.5 m/s

Using the equation derived above, we can calculate the velocity of the raft with the person:

velocity of raft with person = [(mass of raft * velocity of raft) + (mass of person * velocity of person)] / (mass of raft + mass of person)

Substituting the given values:

velocity of raft with person = [(100 kg * 1 m/s) + (50 kg * 1.5 m/s)] / (100 kg + 50 kg)

Simplifying the equation:

velocity of raft with person = [(100 kg + 75 kg) / 150 kg] m/s

velocity of raft with person = 175 kg / 150 kg m/s

velocity of raft with person = 1.1667 m/s

Answer

The velocity of the raft with the person after the jump is approximately 1.1667 m/s.