What is the use (/ meaning) of $F =ma$? I have noticed that Euler's formula for force is useful with a couple of natural forces (at distance), like gravity, that can follow a body any length.
If you consider the most common occurrences of a force, that is the so-called push or pull, I can see little use of that definition, I hope someone can contradict me.
Even the longest human arm can extend for less than one meter and, in that limited span of space and time, reach a modest acceleration up to 20/30m/s.
But the most striking feature of the formula $F=ma$ is that it doesn't say anything about the applied force, but can only measure its oucome. Suppose we say that a basketball player/shot putter exerts a force of 200 N for 1/4 sec, in theory that means a change of momentum of 50 kgm/s but actually we know nothing of what will really happen when a shot or a basket ball or a ping-pong ball is launched. 


*

*we know nothing of the energy that was spent, 

*of the energy the object will acquire; 

*we know nothing of the change of velocity of the object, and 

*we can't even be sure that the change of momentum will actually be 50, since there is a limit to the acceleration due to the max v reached by the hand/ fingertips (therefore the momentum of a ping-pong ball can be at most, say, 1 kgm/s).


Am I missing something really important, or is Euler's (*) formula rarely of great use? 
Edit:
The question has been misinterpreted: it is neither aggressive nor too broad, but very simple. It draws the attention on the fact that in dimensional analysis different entities may have same units.
$F*t$ has the same units of momentum but cannot be totally identified with it for many reasons, one being the one I pointed out, that it carries less information than a real momentum J = m * v.
The simple question: "determine the velocity or Kinetic energy of an object to which a push, a so-called "impulse" J = 50 Kgm/s (F = 200 N , t = .25 sec) is given" , has not received a concrete answer, only generic, formulas.
If determining the force exerted by muscles is considered the problem, you may consider a compressed - released spring:



*

*The force constant is: k = 200N/m, and the time the force acts is 0.4 sec, can someone determine the energy the brown block will acquire? That is a very narrow, specific question.

*Even if we knew the mass of the block which is pushed by the spring, can we determine its v or Ke? If we put a mass A = 0.1 Kg then a mass B of 0.2 Kg, will A acquire a speed which is double of mass B's?
The answers are very simple, too,don't require lectures. If I was right, just say so, if I am wrong just write the values of v and Ke and briefly explain, if you think it is necessary.

* Note: 
nobody ever refers to it as Jakob Hermann's law. Newton knew his interpretation but repudiated it
 A: This answer is a bit aggressive. Then again, so is the question.

Euler's formula for force

It's erroneous to attribute $F=ma$ to Euler. Even though Newton never wrote $F=ma$ in his Principia, this statement is almost universally recognized as Newton's second law. As far as I can tell, it was Jakob Hermann who first expressed Newton's words in an algebraic statement akin to $F=ma$. But that's all an aside best left to the sister site, History of Science and Mathematics.


We know nothing of the energy that was spent, or of the energy the object will acquire.

Sure we do. There's an intimate relation between work and energy. The work-energy principle says that the change in the kinetic energy of an object is equal to the net work done on the object. Net work is given by $W=\int \vec F \cdot d\vec l$, where the force on the right hand side is the same force described by $\vec F=m\vec a$.


Am I missing something really important, or is Euler's formula rarely of great use?

In addition to the work-energy principle, you are missing many things of great importance. And contrary to what you said, $F=ma$ is frequently of great use. Many, if not most, fields of engineering can be viewed as applied classical mechanics. Describing where $F=ma$ (and related concepts) are of exceptionally great use would require multiple college classes, plus a library full of books and technical papers, plus conferences and workshops that occur on a daily basis in college campuses and elsewhere, plus consulting tens, maybe hundreds of thousands of people worldwide who use Newtonian mechanics on a regular basis in their work. Asking where $F=ma$ is of great use is too broad of a topic for a Q&A site such as this.
While $F=ma$ is (perhaps erroneously) used as a short-and-simple stand-in for all of Newtonian mechanics, there's a lot more to classical mechanics than $F=ma$. Even in a strictly Newtonian sense, you are missing two other key concepts:


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*Newton's third law of motion, which describes the behaviors of individual forces, and

*The superposition principle, which dictates that the net force on an object is the vector sum of the individual forces on an object.


Going beyond Newtonian mechanics, but staying well within the realm of classical mechanics, you are also missing (not a complete list):


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*The work-energy principle, described above;

*D'Alembert's principle, which is widely used in robotics (e.g., Kane's equations of motion) to describe motions subject to constraints,

*Lagrangian and Hamiltonian mechanics, which are Newtonian mechanics rewritten from the perspective of energy.



Finally, I suggest you watch this short (3 minute) youtube video that features a professional physicist and that describes a robot that emulates a sandfish. Count the number of times the word "force" (and related terms such as "drag") is used: https://www.youtube.com/watch?v=Rwoz4WbXxdI . This represents but one of an extremely vast number of the applications of $F=ma$.
A: You are missing something very important.
$$ F(x,\dot{x},t) = m\ddot{x}(t)$$
is a differential equation that, given that we know the forces that act, completely determines what will happen (unless the equation has multiple possible solutions, but almost all cases of application turn out to be well-behaved), i.e. the trajectory $x(t)$ from initial conditions $x(0),\dot{x}(0)$.
So we indeed can know everything - even the things you claim we know nothing of, since they're just functions of $x(t)$ and its derivatives - just by solving $F = ma$.
