Final answer:
The magnitude of the force that a person exerts on a crate to move it at a constant velocity across a rough surface is equal to the magnitude of the frictional force exerted by the floor. Thus, the option a is the correct answer.
Step-by-step explanation:
When a crate is pushed by a person at a constant velocity along a rough, horizontal floor, it implies that the forces acting on the crate are balanced. In accordance with Newton's first law of motion, if an object is moving at a constant velocity, the net force acting on it must be zero. Thus, the magnitude of the force the person exerts on the crate must be equal to the magnitude of the frictional force exerted by the floor on the crate.
In this case, the correct answer to the student's question would be (a) Equal. The force the person applies to the crate and the friction force opposing the movement are of the same magnitude, which keeps the crate moving at a constant velocity.