How to Calculate the Velocity of an Object Dropped Based on Height

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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.

Conservation of Energy

    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.

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

    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.

Height and Velocity Functions

    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.

    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.

    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.

    Tips

    • If you are able to time how long it takes the object to fall, simply multiply that time by the acceleration due to gravity to find the final velocity.

      If you want to know the velocity of the object at some point before it hits the ground, use the distance the object has fallen at that point in place of the distance to the ground in either equation.

      Multiply feet per second by 0.68 to find the object's velocity in miles per hour.

    Warnings

    • These equations do not apply to objects dropped from very high up, because such objects will reach a terminal velocity before they hit the ground. If you know the terminal velocity of an object, divide that number by the square root of 2*g to determine the maximum height for which these equations will be valid for that object.

References

About the Author

Petra Wakefield is a writing professional whose work appears on various websites, focusing primarily on topics about science, fitness and outdoor activities. She holds a Master of Science in agricultural engineering from Texas A&M University.

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