Answer :

Final answer:

The problem refers to the conservation of momentum. The horizontal recoil velocity of the student as he throws his hat is calculated using the formula for momentum; it is equal in magnitude and opposite in direction to the hat's momentum.

Explanation:

This problem is related to the conservation of momentum. In this case, the student and his hat can be considered as one system, and because there is no external force acting on this system, the total momentum of the system remains constant before and after the hat is thrown away.

Before the hat is thrown, the total momentum of the system is simply the momentum of the student standing still, which is zero. Then, as the hat is thrown, to conserve the total momentum at zero, the student will have a recoil momentum equal in magnitude and opposite in direction to the momentum of the hat. Given that the direction of the throw of the hat is horizontal, the direction of the recoil of the student will also be horizontal. Hence, the term 'recoil velocity' in the question.

The formula for momentum is momentum = mass x velocity, so the recoil velocity = - (momentum of the hat / mass of the student). Remember, the negative sign signifies the opposite direction. Without the specifics of the velocity or direction of the hat throw, we cannot compute the actual numerical magnitude of the recoil velocity.

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