14. A 3.0 kg metal ball, at rest, is hit by a 1.0 kg metal ball moving at 4.0 m/s. The 3.0 kg ball moves forward at 2.0 m/s and the 1.0 kg ball bounces back at 2.0 m/s.
(a) What is the total kinetic energy before the collision?

The kinetic energy before the collision was 8 J

Explanation:

The given parameters are;

The mass of the metal ball at rest, m₁ = 3.0 kg

The velocity of the ball at rest = 0 m/s

The mass of the metal ball that hits the one at rest, m₂ = 1.0 kg

The velocity of the metal ball that hits the one at rest, v₂ = 4.0 m/s

The velocity with which the 3.0 kg ball moves forward = 2.0 m/s

The velocity with which the 1.0 kg ball bounces back = 2.0 m/s

a) Kinetic energy, K.E. = 1/2 × m × v²

Where;

m = The mass of the of the object in motion

v = The velocity of the object

Before the collision, we have;

Initial K.E. = 1/2 × m₁ × v₁² + 1/2 × m₂ × v₂²

∴ Initial K.E. = 1/2 × 3.0 kg × (0 m/s)² + 1/2 × 1.0 kg × (4.0 m/s) ² = 8 J

The kinetic energy before the collision = The initial K.E. = 8 J.

d.7.5cm is your answer