The whip would be around 10–11 feet long and most likely made from some steel alloy. If we were to ignore the strength limitations of humans and assume that someone could actually effectively use this theoretical whip as they would a normal one, would it be able to crack the same way that a whip usually does. Could this solid metal whip produce firearm like ballistics if the tip had the same mass as a rifle caliber round, and would the whip be able to survive the forces at play and not destroy itself. (plz ignore my horrible grammar, I'm an engineer in training and should probably be studying for my exam instead of asking this question).
And the reason I say no will come across as quite nit-picky, but I think it's rather relevant.
Assuming for the moment that at the moment the Whip cracks, the tip departs the whip with the same velocity/energy as your 5.56 round - there are 3 immediate problems which is why I say the ballistics will not be the same.
1: The direction of travel vs the shape of the whip tip.
So with your bullet - it's shaped to be aerodynamic (ignoring WW1 inverted rounds) in the direction of travel. Pointy at one end, spitzer'd at the other - nice.
Your whip crack tip however - assuming one is able to crack it in such a manner as to accurately in the desired direction would most likely shear off the end - even if this is by design - you first have the problem of uneven breakage - but worst of all - you don't have a means of controlling exactly when the break will be and what angle the now projectile will have relative to it's trajectory. It could be nice and aligned - but more likely it's going to be at an angle - this is going to impact your Ballistics.
2: Barrel length vs indeterminacy of the above.
So, for a rifle - we have Barrel length and the sight radius and various other things to try and make sure that everything is as tightly aligned as possible 1 degree offset at 100 yards is 5.2 feet - that's more than a Human's width. Realistically - a good quality 5.56 platform with 1 MOA is accurate to 0.16 degrees.
I don't think it's feasible that someone could crack a whip and have a projectile detach within such a narrow window.
The big thing about Rifles is that they are... Rifled! those grooves in the Barrel aren't there to increase manufacturing costs - nope - they spin the projectile and impart a degree of stability for the projectile that leads to predictability - the Bullet goes in approximately the direction you want it.
Your Whip crack, if it's going to spin at all, it likely to spin/tumble in the direction of flight, rather than perpendicular to it (like a rifle round) - this combined with the angle of the projectile when it breaks relative to the direction of travel means your projectile will probably be similar enough as makes no difference within a short distance - but air drag and tumbling and lack of stability etc. etc. will mean significantly different Ballistics
Here is a supersonic trebuchet video. It has a fair amount of physics in it if you are interested. So, the speeds are possible. It does not spin what it launches, but this was never the aim of the thing. But at least the velocity part of the problem has been comprehensively answered.