Question

Is a bullet fired by a gun more dangerous than bullet fire with medium speed? Explain it properly.

Answer 1

Hint: This question is based on the combination of the concepts of the conservation of the momentum and Newton’s third law of motion. So, we will make use of these concepts, that is, the final momentum equals the initial momentum (the conservation of the momentum) and, thus, we will have the bullet fired (action) recoils (reaction), that is, Newton’s third law.

Complete answer:
When we fire the bullet by a gun, the gun recoils with equivalent force. Thus, the momentum is conserved, that is, the momentum of the bullet fired equals the momentum of the recoil of the gun.

As, we know that, the momentum is the product of the mass and velocity, so, we have,
 The momentum of the bullet fired = The momentum of the recoil of the gun.
\[{{m}_{i}}{{v}_{i}}={{m}_{f}}{{v}_{f}}\]

The above equation also represents Newton’s third law of motion, that is, the force with which the bullet gets fired out of the gun equals the force with the gun recoils. The action, that is, the bullet fired by the gun, equals the reaction, that is, the gun gets recoiled.

So, we can say that the bullet fired by a gun will have more speed than the bullet fired with a medium speed.

\[\therefore \] The bullet fired by a gun is more dangerous than bullet fire with medium speed.

Note: This is a direct question, but with confusion, because they didn’t mention anything about recoiling the gun. So, at first glance, the question seems to be difficult. As the momentum of the bullet fired equals the momentum of the recoil of the gun, thus, the bullet fired with a medium speed will have the least momentum of the recoil of the gun when compared to that of the bullet by a gun.