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.
