Final answer:
The height of the building the stone was dropped from can be found using the free fall equation d = ½ g t². Substituting the known values, the height is calculated to be 122.5 meters.
Step-by-step explanation:
To determine how tall the building is, we must use the equations of motion that describe free fall. The distance (d) an object falls due to gravity when it starts from rest is given by the equation:
d = ½ g t²,
where g is the acceleration due to gravity (9.8 m/s²) and t is the time in seconds. Plugging in our values, we have:
d = ½ (9.8 m/s²) (5 s)²,
d = ½ (9.8 m/s²) (25 s²),
d = (4.9 m/s²) (25 s²),
d = 122.5 m.
Therefore, the height of the building the stone was dropped from is 122.5 meters.
Free fall refers to the motion of an object falling under the influence of gravity, experiencing acceleration without any air resistance. In this scenario, the only force acting on the object is gravity, causing it to accelerate towards the Earth at approximately 9.8 meters per second squared. The object's velocity increases as it falls, but air resistance becomes significant at higher speeds. In a vacuum, without air resistance, all objects experience the same acceleration regardless of mass, leading to the principle of equivalence between gravitational and inertial mass. Free fall is a fundamental concept in physics, crucial for understanding gravitational forces and acceleration due to gravity.