Final answer:
The ratio of the masses of the objects m₂:m₁ is 2:1. In this scenario, two objects collide and move with equal speed in opposite directions.
Step-by-step explanation:
In this scenario, we have two objects colliding with each other. T
he object with mass m₁ collides with the object at rest, which has mass m₂.
After the collision, the objects move with equal speed in opposite directions.
We need to find the ratio of the masses m₂:m₁.
To solve this problem, we can use the law of conservation of momentum.
According to this law, the total momentum before the collision is equal to the total momentum after the collision.
Since the object with mass m₂ is initially at rest, its initial momentum is zero.
Let's denote the initial speed of the object with mass m₁ as v₁ and the final speed of both objects as v'.
Using the law of conservation of momentum, we can write the equation:
m₁v₁ = m₁v' - m₂v'
We know that the objects move with equal speed in opposite directions, so v' = -v₁.
Substituting this value into the equation, we get:
m₁v₁ = -m₁v₁ - m₂(-v₁)
Simplifying the equation further, we get:
m₁v₁ + m₁v₁ + m₂v₁ = 0
m₁(2v₁) + m₂v₁ = 0
(2m₁ + m₂)v₁ = 0
Since v₁ cannot be equal to zero, we must have:
2m₁ + m₂ = 0
Therefore, the ratio of the masses m₂:m₁ is 2:1.