Speed has only magnitude and no direction.
The Law of Conservation of Energy
You can use the impulse momentum theorem and just subtract the two momenta.
P1 - P2 = (16-1.2)(11.5e4)=1702000Ns
If you first worked out the force and integrated it over time the result is the same
(a) +9.30 kg m/s
The impulse exerted on an object is equal to its change in momentum:

where
m is the mass of the object
is the change in velocity of the object, with
v = final velocity
u = initial velocity
For the volleyball in this problem:
m = 0.272 kg
u = -12.6 m/s
v = +21.6 m/s
So the impulse is

(b) 155 N
The impulse can also be rewritten as

where
F is the force exerted on the volleyball (which is equal and opposite to the force exerted by the volleyball on the fist of the player, according to Newton's third law)
is the duration of the collision
In this situation, we have

So we can re-arrange the equation to find the magnitude of the average force:

The energy of the wave decreases gradually