How to Find Velocity From Mass & Height

How to Find Velocity From Mass & Height
••• German-skydiver/iStock/GettyImages

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.


    • 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.

Related Articles

Cool Gravity Experiments
How to Calculate Resultant Velocity
How to Calculate a Change in Momentum
How Does the Force of Momentum Affect an Object in...
How the Mass of an Object Affects Its Motion
How to Find Acceleration in G's
How Did Isaac Newton Discover the Laws of Motion?
How to Calculate the Distance/Speed of a Falling Object
How to Calculate the Velocity of an Object Dropped...
What Happens As an Object Falls Toward Earth?
How to Calculate the Change in Internal Energy
How to Find the Inertia of an Object
What is Inertia?
How to Calculate Momentum After a Collision
How to Calculate Inertial Force of Mass
The Physics of Egg Drop Science Projects
Difference Between Velocity Time Graph & Position Time...
How to Calculate Angular Acceleration
How to Calculate How Long it Takes an Object to Fall