Question

Телега массой 120 кг катится со скоростью 6 м/с. Человек бежит на встречу телеге со скоростью 9 км/час и прыгает в телегу. С какой скоростью будет двигаться телега после этого,если масса человека 60 кг?

Answer 1

M1v1-m2v2=v(m1+m2) выражаем v, и получаем ответ 1м/с

Answer 2

Problem Analysis

We are given the following information: - Mass of the cart (telega): 120 kg - Speed of the cart: 6 m/s - Speed of the person running towards the cart: 9 km/h - Mass of the person: 60 kg

We need to find the speed of the cart after the person jumps into 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 into the cart is equal to the total momentum after the person jumps into the cart.

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 of the object - v is the velocity of the object

Let's denote the mass of the cart as m1, the velocity of the cart as v1, the mass of the person as m2, and the velocity of the person as v2.

Before the person jumps into the cart, the total momentum is given by:

Total momentum before = (m1 * v1) + (m2 * v2)

After the person jumps into the cart, the total momentum is given by:

Total momentum after = (m1 + m2) * v

According to the principle of conservation of momentum, the total momentum before is equal to the total momentum after. Therefore, we can set up the following equation:

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

We can rearrange this equation to solve for v, the velocity of the cart after the person jumps in:

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

Now let's substitute the given values into the equation and calculate the velocity of the cart.

Calculation

Given: - Mass of the cart (m1): 120 kg - Velocity of the cart (v1): 6 m/s - Mass of the person (m2): 60 kg - Velocity of the person (v2): 9 km/h

Converting the velocity of the person from km/h to m/s: v2 = 9 km/h * (1000 m/1 km) * (1 h/3600 s) = 2.5 m/s

Substituting the values into the equation: v = ((120 kg * 6 m/s) + (60 kg * 2.5 m/s)) / (120 kg + 60 kg)

Simplifying the equation: v = (720 kg*m/s + 150 kg*m/s) / 180 kg

Calculating the velocity: v = 870 kg*m/s / 180 kg = 4.83 m/s

Answer

Therefore, the cart will move with a velocity of 4.83 m/s after the person jumps into it.

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