Final answer:
It is false that the boy must have been pushing with a force of exactly 100 N to move a 300 N box up a 1.0 m high and 3.0 m long ramp.
Step-by-step explanation:
The statement that the boy must have been pushing with a force of exactly 100 N because the ramp was 1.0 m high and 3.0 m long is false. This is because the work done to lift the box to a certain height does not directly correlate to the force applied along the ramp.
The actual force required can be less than the weight of the box because the ramp, which is a type of inclined plane, allows the input force to be spread over a longer distance.
The mechanical advantage gained with the inclined plane reduces the amount of force needed to lift the box to the same height compared to lifting it straight up. However, if friction is present, which it typically is, the boy would have to exert additional force to overcome it.