Understanding the Concepts
* Perfectly Elastic Collision: A collision where both momentum and kinetic energy are conserved.
* Conservation of Momentum: The total momentum of a system remains constant before and after a collision.
* Conservation of Kinetic Energy: The total kinetic energy of a system remains constant before and after a collision.
Let's set up the problem:
* Mass of each glider: m
* Initial velocity of glider 1: v₁
* Initial velocity of glider 2: -v₁ (opposite direction)
Applying Conservation of Momentum:
* Initial momentum: mv₁ + m(-v₁) = 0
* Final momentum: mv₁' + mv₂' = 0 (where v₁' and v₂' are the final velocities)
Since the initial momentum is zero, the final momentum must also be zero. This gives us:
v₁' + v₂' = 0
Applying Conservation of Kinetic Energy:
* Initial kinetic energy: (1/2)mv₁² + (1/2)m(-v₁)² = mv₁²
* Final kinetic energy: (1/2)mv₁'² + (1/2)mv₂'²
Equating initial and final kinetic energy:
mv₁² = (1/2)mv₁'² + (1/2)mv₂'²
Solving for Final Velocities:
1. From the momentum equation: v₁' = -v₂'
2. Substitute this into the energy equation: mv₁² = (1/2)m(-v₂')² + (1/2)mv₂'²
3. Simplify: mv₁² = mv₂'²
4. Solve for v₂': v₂' = v₁
5. Substitute back into the momentum equation to find v₁': v₁' = -v₁
Conclusion:
The final velocities of the two gliders are:
* Glider 1 (originally moving with velocity v₁): v₁' = -v₁ (The glider reverses direction and maintains its speed)
* Glider 2 (originally moving with velocity -v₁): v₂' = v₁ (The glider also reverses direction and maintains its speed)
In a perfectly elastic collision between two objects of equal mass and opposite initial velocities, they simply exchange velocities.
