To determine the height of the building, we can use the equations of motion for an object in free fall.
The relevant equation in this case is:
v² = u² + 2as
where: v = final velocity (45 m/s, downward) u = initial velocity (0 m/s, as the stone is dropped) a = acceleration due to gravity (-9.8 m/s², assuming negligible air resistance) s = displacement (height of the building)
Substituting the given values into the equation, we can solve for the height of the building:
45² = 0² + 2 * (-9.8 m/s²) * s
2025 = -19.6s
Dividing both sides of the equation by -19.6:
s = 2025 / -19.6 ≈ -103.3163 meters
The negative sign indicates that the displacement is in the downward direction, which is appropriate since the stone is dropped from the top of the building.
Therefore, the height of the building is approximately 103.3163 meters.