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?

initial kinetic energy = final kinetic energy = m · v²

Explanation:

Hi there!

Since the gliders collide elastically, the kinetic energy and momentum of the system after the collision are the same as before the collision.

Then, the initial kinetic energy of the system will be equal to the final kinetic energy of the system.

The equation of kinetic energy for each glider is the following:

KE = 1/2 · m · v²

Where:

KE = kinetic energy.

m = mass of the glider.

v = velocity of the glider.

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

initial 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 equation of momentum of the system:

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

The initial and final momentum of the system is zero because both vectors cancel each other for being of the same magnitude but of opposite direction.