Question

Тележка массой 50кг движется в горизонтальном направлении со скоростью 2м/с . С тележки соскакивает человек со скоростью 4 м/с относительно земли в направлении , противоположном движению тележки . Масса человека 70 кг . Какова скорость тележки после того , как человек с нее спрыгнул ?

Answer 1

P1+p2= const
m1=50 кг
m2=70 кг
V1=2 м/с
V2=4 м/с
V-искомое
(m1+m2)*v1=v*m1-v2m2, 
p1=(50+70)*2=240
50*v-70*4=240; 50*v-280=240; 50*v=520; v=10,4 (м/с)

Answer 2

Problem Analysis

We are given a cart with a mass of 50 kg moving horizontally with a velocity of 2 m/s. A person with a mass of 70 kg jumps off the cart with a velocity of 4 m/s in the opposite direction of the cart's motion. We need to determine the velocity of the cart after the person jumps off.

Solution

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

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 cart after the person jumps off as V. The momentum before the person jumps off is the sum of the momentum of the cart and the momentum of the person. The momentum after the person jumps off is the momentum of the cart alone.

Before the person jumps off: Total momentum = (mass of cart) * (velocity of cart) + (mass of person) * (velocity of person)

After the person jumps off: Total momentum = (mass of cart) * (velocity of cart after) Since the total momentum before and after the person jumps off is the same, we can equate the two expressions and solve for the velocity of the cart after