How To Calculate Velocity Of Falling Object

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.

Step 1

Convert all units of time to seconds. For example, an object that falls for 850 milliseconds falls for 0.850 seconds.

Step 2

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.

Step 3

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.

Step 1

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.

Step 2

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.

Step 3

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.