because wiith the 45 degree angle we are going to have an optimal blend between horizontal and vertical velocities

I agree with IntelInside... a 45 degree angle is the optimal blend. Here's an example (slightly modified) taken from EK 1001

A projectile is launched at an angle of 30 degrees to the horizontal. It's initial velocity is 20m/s. How far does it travel?

To solve this you have to first find total flight time. Using v=vo+at where v=0m/s at the top of the flight path; vo=vo(sin30); and a=-10m/s

We see that t=1 sec

That's only for half the trip though so total flight time is t=2 sec

Now to find total distance traveled we can use the equation d=vot+1/2at^2

Where a=0 because there's no acceleration in the x-direction; t=2 sec; and vo=vo(cos30)

We see that d=36m

Now, do the same problem with a 45 degree angle.

We see that t=3.4 sec and d=57.8m

Well, what about a 60 degree angle?

We see that t=3.6 sec and d=36m

A 45 degree angle is clearly the magic angle that maximizes travel time and distance.