Question

Two billard balls move toward one another.The balls have identical masses, and the collision is perfectly elastic. The initial velocity of the balls are +30 cm/s and -20 cm/s, what is the velocity of each ball after the collision?

Answer 1

Use conservation of momentum, and conservation of kinetic energy for an elastic collision.

m*30 + m*-20 = m*v1 + m*v2
where v1 is the final speed of the first ball, v2 is the final speed of the second ball
Simplifying the equation (dividing both sides by m, adding like terms)

10 = v1 + v2


Conservation of kinetic energy:

1/2*m*30^2 +1/2*m*(-20)^2 = 1/2*m*v1^2 + 1/2 *m*v2^2

or

90 + 40 = 130 = v1^2 + v2^2

You have two equations with two unknowns:

10 = v1 + v2
130 = v1^2 + v2^2

Use algebra to solve for v1 and v2