How to Find Velocity From Mass & Height

By John Brennan
Gravity pulls falling objects toward Earth.

Back in the Middle Ages, people believed that the heavier an object, the faster it would fall. In the 16th century, Italian scientist Galileo Galilei refuted this notion by dropping two metal cannonballs of different sizes from atop the Leaning Tower of Pisa. With the help of an assistant, he was able to prove that both objects fell at the same speed. Earth's mass is so large compared to your own that all objects near Earth's surface will experience the same acceleration -- unless they encounter substantial air resistance. (A feather, for example, would clearly fall much slower than a cannonball.) To determine a falling object's velocity, all you need is its initial upward or downward velocity (if it was thrown up into the air, for example) and the length of time it's been falling.

The force of gravity causes objects near Earth's surface to fall with constant acceleration of 9.8 meters per second squared unless air resistance is substantial. Keep in mind that the integral of acceleration over time will yield velocity.

Multiply the length of time the object has been falling by 9.8 meters per second squared. For example, if an object has been in free-fall for 10 seconds, then it would be: 10 x 9.8 = 98 meters per second.

Subtract your result from the object's initial upward velocity. For example, if the initial upward velocity is 50 meters per second, it would be: 50 - 98 = -48 meters per second. This answer is the object's velocity. A negative velocity means it is moving downward (falling), which is exactly what we would expect.

Tip

Eventually, the object will hit the ground and go splat, at which point its velocity will be 0. You can determine when the object will hit the ground by using the following equation:

position = initial height + V T - 4.9 T squared

where T is the length of time elapsed and V is the initial upward velocity.

About the Author

Based in San Diego, John Brennan has been writing about science and the environment since 2006. His articles have appeared in "Plenty," "San Diego Reader," "Santa Barbara Independent" and "East Bay Monthly." Brennan holds a Bachelor of Science in biology from the University of California, San Diego.