Final answer:
Both stones thrown from the same height and with the same speed, one upward and one downward, will land the same distance from the building when air resistance is neglected, as their horizontal motion is unaffected by gravity.
Step-by-step explanation:
Which Stone Lands Farther From The Building?
When two stones are thrown from the same height with the same magnitude of velocity, one thrown upward and the other thrown downward, their situations relate to the principles of projectile motion and free fall. According to physics principles, specifically when neglecting air resistance, both stones are subjected to the same acceleration - the acceleration due to gravity. The initial velocity vectors for the two stones are opposite in direction but equal in magnitude. As a result, the two stones, regardless of the initial throw direction, will land at the same distance from the building provided that they are thrown with the same speed and from the same height. This is because the horizontal component of their motion is unaffected by gravity, and thus the horizontal displacement is unaffected by the direction of the throw.
To illustrate this with an example, let's say both stones are thrown horizontally at the same speed from the same height off a building; the stone thrown upward will ascend to a certain height then descend, while the one thrown downward will just descend. The time it takes for each stone to hit the ground will differ due to their different paths, but their horizontal speeds remain unaffected, ultimately causing them to land the same distance from the building. The vertical motion does not influence the horizontal displacement in projectile motion without air resistance.