If a hammer weighs kg and travels at m/s and impacts a nail at a constant force of N and bounces off at the same velocity, how...

Hello!

Let's start from Newton's Second law, Here is the mass of a hammer, is its acceleration and is the force which acts on it. By Newton's Third law this force is the same in magnitude as the force which acts on a nail, and it is given that it is constant.

Next, recall that acceleration is the derivative of velocity      is for time. Then and we...

Hello!

Let's start from Newton's Second law, Here is the mass of a hammer, is its acceleration and is the force which acts on it. By Newton's Third law this force is the same in magnitude as the force which acts on a nail, and it is given that it is constant.

Next, recall that acceleration is the derivative of velocity      is for time. Then and we can integrate this equality over time interval in question.

At the left side we obtain where is the time we have to determine, at the right side we obtain the change of

Denote the initial speed of a hammer as then the change of is equal to because the velocity was in one direction and becomes in the opposite direction, or and

This way we have  

In numbers it is This is the answer.

That said, it is absolutely impossible that the force was constant. Actually the given value for force means average force during the collision.

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