Question on: JAMB Physics - 2020

Here's how to solve this problem using the principle of conservation of momentum: * **Identify the knowns:** * Mass of the machine gun, *M* = 5 kg * Mass of the bullet, *m* = 50 g = 0.05 kg (convert to kg) * Velocity of the bullet, *v* = 100 m/s * Recoil speed of the machine gun, *V* = ? * **Apply the conservation of momentum:** The total momentum before firing equals the total momentum after firing. Initially, both the gun and the bullet are at rest, so the initial momentum is zero. * Initial momentum = 0 * Final momentum = *M* \* *V* + *m* \* *v* Therefore: 0 = *M* \* *V* + *m* \* *v* * **Solve for the recoil velocity (V):** * *M* \* *V* = - *m* \* *v* * *V* = - (*m* \* *v*) / *M* * *V* = - (0.05 kg \* 100 m/s) / 5 kg * *V* = - 5 kg m/s / 5 kg * *V* = -1 m/s * The negative sign indicates that the machine gun recoils in the opposite direction to the bullet's motion. The magnitude of the recoil speed is 1 m/s.