If two gliders of equal mass m and equal and opposite initial velocity v collide perfectly elastically, using both the momentum and energy conservation equations from equation (71), what is the initial kinetic energy and what is the final kinetic energy, in terms of m and v?

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initial kinetic energy = final kinetic energy = m · v²

Explanation:

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From the collision of the elastic gliders, the kinetic energy and momentum of the system after the collision are the same as before the collision.

The initial kinetic energy of the system will then be equal to the final kinetic energy of the system.

The kinetic energy equation for each glider is as follows:

KE = 1/2 · m · v²

Where:

KE = kinetic energy.

m = mass of the glider.

v = velocity of the glider.

The sum of the kinetic energy of each glider is the kinetic energy of the system. Then, the initial kinetic energy of the system is:

front KE = 1/2 · m · v² + 1/2 · m · v²

initial KE = m · v²

Since the initial kinetic energy of the system is equal to the final kinetic energy of the system:

final KE = m · v²

Using the system momentum equation:

initial momentum = m · v + m · (-v) = m (vv) = 0

The initial and final momentum of the system is zero because the two vectors cancel each other because they are the same size but in a different direction.