Two objects of the same mass travel in the same direction along a horizontal surface. Object X
has a speed of 5 ms
and object Y
has a speed of 2 ms
, as shown in the figure. After a period of time, object X
collides with object Y
.

Consider the situation in which the objects collide but do not stick together. Which of the following predictions is true about the center of mass of the two-object system immediately after the collision?

After the collision, object X will move at a speed of 2 m/s in its original direction while object Y will move at a speed of 5 m/s in its original direction.

Elastic collision of the two objects

When the two objects collide but do not stick together, the type of collision is elastic collision.

In elastic collision, both momentum and kinetic energy are conserved.

Final velocity of the two objects after collsion

mu₁ + mu₂ = mv₁ + mv₂

5m + 2m = mv₁ + mv₂

m(5 + 2) = m(v₁ + v₂)

7 = v₁ + v₂ -------- (1)

Apply the concept of one direction velocity;

u₁ + v₁ = u₂ + v₂

5 + v₁ = 2 + v₂

v₂ = v₁ + 3 ------ (2)

Solve (1) and (2) together;

7 = v₁ + v₁ + 3

4 = 2v₁

v₁ = 2 m/s

v₂ = 2 + 3 = 5 m/s

Thus, after the collision, object X will move at a speed of 2 m/s in its original direction while object Y will move at a speed of 5 m/s in its original direction.

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