Final answer:
In the absence of air resistance, an object launched horizontally from a given height will take the same time to reach the ground as an object dropped directly. Thus, an object launched with any horizontal velocity from a height of 31.7 meters will hit the ground in 2.54 seconds.
Step-by-step explanation:
The subject of the student's question is Physics, and it falls under the category of Projectile Motion which is a typical topic in a high school physics curriculum. The time taken for an object to hit the ground when dropped is independent of its horizontal velocity, because the horizontal and vertical motions are independent of each other. This is due to gravity acting only in the vertical direction. Given that one object took 2.54 seconds to drop from a vertical distance of 31.7 meters, any other object, regardless of its horizontal velocity, will take the same amount of time (2.54 seconds) to fall that vertical distance, if air resistance can be neglected. Therefore, an object launched with a horizontal velocity of 500 m/s from the same height will take 2.54 seconds to hit the ground, just like the object that was dropped.