You just didn't give the correct expression for what you claim the answer should be. An elastic collision is a type of collision in which kinetic energy is conserved. This means that the total energy of the system before and after the collision remains the same.
In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum of the system before the collision is equal to the total momentum after the collision.
Yes, the simple derivation for elastic collisions involves using the conservation of momentum and conservation of kinetic energy equations. By setting the initial and final momenta and kinetic energies equal to each other, you can solve for the final velocities of the objects involved.
The most common mistake people make when deriving elastic collisions is forgetting to include the mass of the objects in the equations. The mass is a crucial factor in calculating the final velocities of the objects after the collision.
Yes, there are many real-life examples of elastic collisions. Some examples include billiard balls colliding on a pool table, a rubber ball bouncing off the ground, and two cars colliding and bouncing off each other without causing damage.