A ball with a mass of #6# #kg # and velocity of #7# #ms^-1# collides with a second ball with a mass of #4# #kg# and velocity of #- 8# #ms^-1#. If #15%# of the kinetic energy is lost, what are the final velocities of the balls?
1 Answer
Momentum is conserved, but because this is an inelastic collision kinetic energy is not. The final velocities of the masses are:
Explanation:
Before the collision:
After the collision
Because momentum is always conserved, the momentum of the system after the collision will still be
We can now set up a system of simultaneous equations.
After the collision:
We can use the first equation to express
We can then substitute that expression into the second equation, so that it will be in only one variable:
The algebra is a bit messy to do and mark up here, so I might leave that as an exercise for you to do. It's just math, not physics.
Because it's a quadratic equation it yields two solutions,
Let's see what they lead to in terms of
If
If
Both sets of solutions actually make sense.