When two colliding objects are at rest, say, a book on a table, the normal force the table exerts on the book will exactly cancel out the force of gravity (or other forces) the book exerts on the table. Due to that, I've been subconsciously assuming that these forces are present in that exact manner as soon as the two objects collide, assuming a perfectly elastic collision.
However, thinking about it more, that clearly seems wrong: If the normal force at the exact time of impact was only equal to the downwards force, the net force acting on the book would be 0, and by Newton's 1st Law, the book would continue travelling at a constant speed through the table - which is wrong.
Therefore, I assume the normal force exerted on the book at the time of impact is much higher than the downwards force, and reduces over time to be equal to it.
The question I have is as follows: What is the normal force at the time of impact? How do I calculate it? Where does it come from?
Maybe something to do with conservation of linear momentum? The problem there is that I don't really have a "time of impact" if I consider my impact to be an instant (Or, alternatively, extremely long given that the book stays on the table) I'm honestly confused.