How To Calculate The Velocity Of An Object Dropped Based On Height

Acceleration due to gravity causes a falling object to pick up speed as it travels. Because a falling object's speed is constantly changing, you may not be able to measure it accurately. However, you can calculate the speed based on the height of the drop; the principle of conservation of energy, or the basic equations for height and velocity, provide the necessary relationship. To use conservation of energy, you must balance the potential energy of the object before it falls with its kinetic energy when it lands. To use the basic physics equations for height and velocity, solve the height equation for time, and then solve the velocity equation.

Step 1

Ascertain the height from which the object fell. Multiply the height by the object's acceleration due to gravity. The acceleration due to gravity is 32.2 ft/s^2 for English units, or 9.8 m/s^2 for SI units. If you drop an object from 15 feet, for example, you would multiply 15 ft * 32.2 ft/s^2 to get 483 ft^2/s^2.

Step 2

Multiply the result by 2. For example, 483 ft^2/s^2 * 2 = 966 ft^2/s^2.

Step 3

Take the square root of the previous result to calculate the velocity when the object hits the ground. The square root of 966 ft^2/s^2 is 31.1 ft/s, so the object in this example would hit the ground traveling at 31.1 ft/s.

Step 1

Ascertain the height from which the object fell. Multiply the height by 2, and divide the result by the object's acceleration due to gravity. If the object fell from 5 m, the equation would look like this: (2*5 m)/(9.8 m/s^2) =1.02 s^2.

Step 2

Take the square root of the result to calculate the time it takes for the object to drop. For example, the square root of 1.02 s^2 equals 1.01 s.

Step 3

Multiply the time by the acceleration due to gravity to find the velocity when the object hits the ground. If it takes 9.9 seconds for the object to hit the ground, its velocity is (1.01 s)*(9.8 m/s^2), or 9.9 m/s.