How to Calculate Terminal Velocity of a Falling Object

Written by alison rohde
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How to Calculate Terminal Velocity of a Falling Object
This skydiver will most likely reach terminal velocity before he pulls his chute. (Thinkstock Images/Comstock/Getty Images)

By definition, an object hits its terminal velocity when it reaches the point in its fall when it is travelling at a constant rate. The shape and mass of the object, as well as the medium it is travelling through, influence the terminal velocity. If the mass and dimensions of the object are known, some simple math will provide a value for terminal velocity.

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  1. 1

    Write out the equation for terminal velocity, which is Vt = √(2mg/CρA), where m is mass, g is gravity, C is drag, ρ is air density, and A is the cross-sectional area of the object.

  2. 2

    Write out all variables in a table. This step will keep them organised while you are solving the problem. Values for the drag coefficients of different objects and for air density are listed in most basic engineering tables. For this example, the falling object will be a sphere falling through air with a temperature of 20 degrees Celsius. The values will be as follows: m = 8kg; g = 9.8m/s2; C = 0.5; ρ = 1.205kg/m3; and A = 0.1 m2.

  3. 3

    Plug the values into the equation: Vt = √(2mg/CρA) = √{(289.8)/(0.51.2050.1)}

  4. 4

    Finish out the math or put the equation into a calculator to solve. The final answer in this example is this: Vt = √{(289.8)/(0.51.2050.1)} = √(156.8)/(0.06025) = √2602.5 = 51 m/s

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