Two identical balls P and Q having velocities $0.7 m s^{-1}$ and $-0.4 m s^{-1}$ respectively are colliding in one dimension elastically. The velocities of P and Q after the collision respectively are:
Step 1: Note the data. Two identical balls P and Q collide head on. P moves at $0.7$ m/s and Q at $-0.4$ m/s in the opposite direction. The collision is elastic.
Step 2: Recall the special rule for equal masses. When two bodies of the same mass collide elastically in one dimension, they simply swap their velocities. This is a famous and very handy shortcut.
Step 3: See why the swap happens. Elastic collisions conserve both momentum and kinetic energy. Solving those two equations for equal masses always gives the exchange of velocities.
Step 4: Apply the swap to P. After the hit, ball P takes Q's old velocity, so P now moves at $-0.4$ m/s.
Step 5: Apply the swap to Q. Ball Q takes P's old velocity, so Q now moves at $0.7$ m/s.
Step 6: State the final pair. So P becomes $-0.4$ m/s and Q becomes $0.7$ m/s. \[ \boxed{-0.4 \ \text{m s}^{-1}, \ 0.7 \ \text{m s}^{-1}} \]
