Both momentum and kinetic energy are conserved in elastic collisions (assuming that this collision is perfectly elastic, meaning no net loss in kinetic energy)
To find the final velocity of the second ball you have to use the conversation of momentum:
*i is initial and f is final*
Δpi = Δpf
So the mass and velocity of each of the balls before and after the collision must be equal so
Let one ball be ball 1 and the other be ball 2
m₁ = 0.17kg
v₁i = 0.75 m/s
m₂ = 0.17kg
v₂i = 0.65 m/s
v₂f = 0.5
m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f
Since the mass of the balls are the same we can factor it out and get rid of the numbers below it so....
m(v₁i + v₂i) = m(v₁f + v₂f)
The masses now cancel because we factored them out on both sides so if we divide mass over to another side the value will cancel out so....
v₁i + v₂i = v₁f + v₂f
Now we want the final velocity of the second ball so we need v₂f
so...
(v₁i + v₂i) - v₁f = v₂f
Plug in the numbers now:
(0.75 + 0.65) - 0.5 = v₂f
v₂f = 0.9 m/s
