A ball with a mass of 3 kg moving at 5 m/s collides with a 9 kg ball at rest. After the collision, the impacting (3 kg) ball bounces back at a speed of 2.5 m/s. How fast does the 9 kg ball move and in what direction

The second ball moves with 0.83 m/s forward.

Explanation:

Given;

mass of the first ball, m₁ = 3 kg

initial velocity of the first ball, u₁ = 5 m/s

final velocity of the first ball, v₁ = 2.5 m/s

mass of the second ball, m₂ = 9kg

initial velocity of the second ball, u₂ = 0

final velocity of the second ball, v₂ = ?

From the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(3x5) + (9x0) = (3x2.5) + (9v₂)

15 = 7.5 + 9v₂

15 - 7.5 = 9v₂

9v₂ = 7.5

v₂ = 7.5/9

v₂ = 0.83 m/s

The second ball moves with 0.83 m/s forward.