Final answer:
The mass will strike the floor with a velocity of approximately 4.1 m/s.
Step-by-step explanation:
To determine the velocity at which a 15kg mass will strike the floor after the rope is cut, we need to use the principle of conservation of energy. Initially, the mass has 250J of energy, which is potential energy due to its height. When it falls to the floor, this potential energy is converted to kinetic energy. We can calculate the kinetic energy using the equation KE = 1/2 mv^2, where m is the mass and v is the velocity. Setting the initial potential energy equal to the final kinetic energy, we have 250J = 1/2 (15kg) v^2. Solving for v, we find v = 4.08 m/s. Therefore, the mass will strike the floor with a velocity of approximately 4.1 m/s.