A 25.0-g object moving to the right at 20.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.

v₁ = 17.1 cm/s

v₂ = 22.1 cm/s

Explanation:

From the principle of linear momentum, the momentum is conserved

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where m₁ = mass of first object = 25.0 g

u₁ = initial velocity of first object = 20 cm/s

m₂ = mass of second object = 10.0 g

u₂ = initial velocity of second object = 15.0 cm/s

v₁ = final velocity of first object

v₂ = final velocity of second object

25 * 20 + 10 * 15 = 25 * v₁ + 10 * v₂

650 = 25v₁ + 10v₂ (1)

Also in an elastic collision, Kinetic energy is conserved and sum of initial and final velocities  is conserved

u₁ + v₁ = u₂ + v₂

20 + v₁ = 15 + v₂

v₂ = 5 + v₁

Substitute v₂ = 5 + v₁ in (1)

650 = 25v₁ + 10(5 + v₁)

90 = 25v₁ + 10v₁ + 50

35v₁ = 600

v₁ = 600/35

v₁ = 17.1 cm/s

Therefore, v₂ = 5 + 17.1 cm/s

v₂ = 22.1 cm/s

their crystal patterns have been disrupted by stress