To find the recoil velocity of a gun when a bullet is fired, the relationship between force, mass, and velocity must be applied using impulse-momentum principles. The problem provides the weights of the bullet and gun, which can be converted to mass using gravitational acceleration. The impulse equation FΔt = mΔv can be rearranged to relate the forces and velocities of both the bullet and gun. Although the initial poster struggles with the unknown mass and time, understanding that the forces acting on both objects are equal and opposite can lead to solving for the recoil velocity. This discussion highlights the importance of impulse concepts and the need to convert weight to mass for accurate calculations.