Final answer:
An investigation involving varying initial conditions or properties of the objects can identify factors affecting the amount of energy transferred during the collision and determine which object transferred the greatest energy to hit the floor.
Step-by-step explanation:
An investigation that can identify factors affecting the amount of energy transferred during the collision can involve varying the initial conditions or properties of the objects and observing the resulting energy transfers. For example, one could investigate the effect of mass on energy transfer by using objects of different masses and measuring the energy transferred when they collide with the floor. Another investigation could involve varying the elasticity of the objects and observing how it affects the energy transfer. By conducting these investigations and analyzing the energy transfers, one can determine which object transferred the greatest energy to hit the floor.