To find the velocity of the second ball after the collision, we can use the principle of conservation of momentum and the law of conservation of kinetic energy. If the collision is elastic, both momentum and kinetic energy will be conserved.
Let's denote the velocity of the second ball as v2 = (v2x, v2y). The mass of both balls is the same.
Using the conservation of momentum, we have:
Initial momentum = Final momentum (mass of first ball) * (initial velocity of first ball) + (mass of second ball) * (initial velocity of second ball) = (mass of first ball) * (final velocity of first ball) + (mass of second ball) * (final velocity of second ball)
(1) 2.5 * I = 0.5 * (0.5i - j) + 1 * (v2x, v2y)
Expanding equation (1), we get:
2.5 * I = 0.25i - 0.5j + (v2x, v2y)
Equating the coefficients of i and j, we have:
2.5 = 0.25 + v2x 0 = -0.5 + v2y
Solving these equations, we find:
v2x = 2.5 - 0.25 = 2.25 v2y = -0.5
So, the velocity of the second ball after the collision is v2 = (2.25i, -0.5j).
To determine if the collision is elastic, we need to compare the initial and final kinetic energies.
Initial kinetic energy = (1/2) * (mass of first ball) * (initial velocity of first ball)^2 Final kinetic energy = (1/2) * (mass of first ball) * (final velocity of first ball)^2 + (1/2) * (mass of second ball) * (final velocity of second ball)^2
Plugging in the given values:
Initial kinetic energy = (1/2) * 1 * (2.5)^2 = 3.125 Final kinetic energy = (1/2) * 1 * (0.5^2 + (-1)^2) + (1/2) * 1 * (2.25^2 + (-0.5)^2) = 1.5 + 2.625 = 4.125
Since the final kinetic energy is greater than the initial kinetic energy, the collision is not elastic.
Therefore, the velocity of the second ball after the collision is v2 = (2.25i, -0.5j), and the collision is not elastic.