Answer to Question #3844 in Mechanics | Relativity for mia

Question

A 0.50 kg ball traveling at 6.0 m/s collides head-on with a 1.00-kg ball moving in the
opposite direction at a velocity of –12.0 m/s.
The 0.50 kg ball moves away at –14 m/s after
the collision. Find the velocity of the second ball.

Answer 1

Let m₁ be the mass of the first ball (m₁ = 0.5 kg), m₂ - the mass of the second ball (m₂ = 1 kg).
U₁, V₁ - speeds of the first ball before and after the collision, U₂, V₂ - speeds of the second ball before and after the collision.
According to the law of conservation of linear momentum (let the initial direction of the first ball be positive):


m₁U₁ - m₂U₂=-m₁V₁ + m₂V₂


V₂ = (U₁ + V₁)*m₁/m₂ - U₂
V₂ = (6 + 14)*0.5/1 - 12 = -2 m/s.


So, the second ball continued moving at the same direction at 2 m/s.