Momentum is P=mv
Let momentum of a be Pa and momentum of b be Pb. Since they are equal we let
Pa=Pb
And we can see that since a is less massive, its velocity is larger than b's.
That is va > vb.
Kinetic energy is E=(1/2)mv^2
Note that using the formula for momentum we can also say kinetic energy is E=(P/2)v
So kinetic energy of a is
Ea=(Pa/2)va
And kinetic energy of b is
Eb=(Pb/2)vb
But we know Pa=Pb so we can substitute this into one of the kinetic energy relations to get
Eb=(Pa/2)vb.
Now putting the two side by side (NOT setting them equal, just comparing them) we get
Ea=(Pa/2)va Eb=(Pa/2)vb
The first part of each equation is the same: Pa/2. The only difference between them is Ea is multiplied va and Eb is multiplied by vb. And because we know va > vb we can conclude that the kinetic energy of a is larger.
