Two objects of different mass dropped from a building -- as purportedly demonstrated by Galileo at the Leaning Tower of Pisa -- will strike the ground simultaneously. This occurs because the acceleration due to gravity is constant at 9.81 meters per second per second (9.81 m/s^2) or 32 feet per second per second (32 ft/s^2), regardless of mass. As a consequence, gravity will accelerate a falling object so its velocity increases 9.81 m/s or 32 ft/s for every second it experiences free fall. Velocity (v) can be calculated via v = gt, where g represents the acceleration due to gravity and t represents time in free fall. Furthermore, the distance traveled by a falling object (d) is calculated via d = 0.5gt^2. Also, the velocity of a falling object can be determined either from time in free fall or from distance fallen.
Convert all units of time to seconds. For example, an object that falls for 850 milliseconds falls for 0.850 seconds.
Calculate the metric solution of velocity by multiplying the time in free fall by 9.81 m/s^2. For an object that falls for 0.850 seconds, the v = 9.81 m/s^2 * 0.850 s = 8.34 m/s.
Determine the imperial solution by multiplying the time in free fall by 32 ft/s^2. Continuing the previous example, v = 32 ft/s^2 * 0.850 = 27.2 ft/s. Consequently, the velocity of the falling object in the example is 27.2 feet per second.
These calculations used are greatly simplified by ignoring air resistance, or drag. Drag must be included in the calculations to find the exact velocity of a specific falling object.
Convert all units of distance fallen to units of feet or meters using on online unit conversion tool. A distance of 88 inches, for example, represents 7.3 feet or 2.2 meters.
Calculate the time during free fall according to t = [d / (0.5g)]^0.5, which represents the equation d = 0.5gt^2 solved for time. For an object that falls 2.2 meters, t = [2.2 / (0.5 * 9.81)]^0.5, or t = 0.67 seconds. Alternatively, t = [7.3 / (0.5 * 32)]^0.5 = 0.68 seconds.
Determine the velocity at the moment of impact according to v = gt. Continuing the previous examples, v = 9.81 * 0.67 = 6.6 m/s or v = 32 * 0.68 = 21.8 ft/s. Consequently, the velocity of the falling object in the example is 21.8 feet per second.
- These calculations used are greatly simplified by ignoring air resistance, or drag. Drag must be included in the calculations to find the exact velocity of a specific falling object.
Thomas Northcut/Lifesize/Getty Images