Final answer:
In a perfectly elastic collision between two identical balls, they will exchange velocities, so the ball initially at 0.75 m/s will end up with -0.43 m/s, and the ball initially at -0.43 m/s will end up with 0.75 m/s.
Step-by-step explanation:
When two identical balls collide head-on in a perfectly elastic collision, the conservation of momentum and kinetic energy apply. The balls will simply exchange velocities because they are identical in mass and the collision is elastic. The first ball with an initial velocity of 0.75 m/s will exit the collision with a final velocity of -0.43 m/s, while the second ball with an initial velocity of -0.43 m/s will take on the initial velocity of the first ball and move at 0.75 m/s post-collision.