Question

Мяч массой 400 г, двигавшийся со скоростью 10 м/с в горизонтальном направлении, попал в неподвижную пластиковую бутылку с водой массой 800 г и отлетел в противоположном направлении.Бутылка приобрела скорость 6 м/с.С какой скоростью отлетел мяч?только можно подробно, с дано и решением.

Answer 1

M1 - масса мяча; m2 - масса бутылки с водой. По закону сохранения импульса тела m1*V1+m2*V2=m1V1'+m2V2' в векторной форме.
Для проекций m1V1+0=-m1V1'+m2V2'
0,4*10=0,8*6-0,4*V1'
0,4V1'=4,8-4
0,4V1'=0,8
4V1'=8
V1'=2 м/с  - ответ.
m1=0,4кг; m2=0,8кг; V1=10м/с; V2=0; V2'=6м/с.

Answer 2

Given Information:

- Mass of the ball (m1) = 400 g = 0.4 kg - Initial velocity of the ball (v1) = 10 m/s - Mass of the plastic bottle with water (m2) = 800 g = 0.8 kg - Final velocity of the bottle (v2) = -6 m/s (negative because it is in the opposite direction)

Solution:

To find the velocity of the ball after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.

Before the collision, the total momentum is the sum of the momentum of the ball and the momentum of the bottle:

Total momentum before = (m1 * v1) + (m2 * 0) (since the bottle is initially at rest)

After the collision, the total momentum is the sum of the momentum of the ball and the momentum of the bottle:

Total momentum after = (m1 * v1') + (m2 * v2')

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

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

Since the bottle is initially at rest, its velocity (v2') after the collision will be zero. Therefore, the equation becomes:

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

Simplifying the equation:

(m1 * v1) = (m1 * v1')

Now we can solve for the velocity of the ball after the collision (v1'):

v1' = (m1 * v1) / m1

Substituting the given values:

v1' = (0.4 kg * 10 m/s) / 0.4 kg

Simplifying:

v1' = 10 m/s

Answer:

The ball rebounds with a velocity of 10 m/s in the opposite direction.