Terminal Velocity Formula

It is a fact that the Earth exerts a gravitational force on every falling object. As some object falls, the force of gravity initially causes it to continuously speed up. When it gets faster and faster, the air drag force increases until eventually. This air drag force is exactly equal to the force of gravity. If these two forces are exactly balanced, then the object will no longer speed up or slow down but will continue falling with some constant velocity. This is the terminal velocity. In this topic, the student will learn the terminal velocity concepts and terminal velocity formula. Let us learn it!

 What is Terminal Velocity?

Since the air drag force depends heavily on the shape and size of the object. Thus objects with a large surface area will have a much lower terminal velocity than the objects with a smaller surface area. The weight of the object will affect the air drag force on the object and, therefore, its terminal velocity.

Source:en.wikipedia.org 

 

The Formula for Terminal Velocity

When an object is falling under the influence of gravity or subject to some type of constant driving force. This force is subject to a resistance or drag force which increases with velocity. It will at last reach the maximum velocity where the drag force equals the driving force. This final, constant velocity of the motion is the “terminal velocity”. This terminology is made popular by the skydivers.

Thus, terminal velocity is defined as the highest velocity which can be attained by an object during its falling through the air. It is possible when the sum of the dragged force i.e. \(F_d\) and buoyancy is equal to the downward force of gravity \(F_G\) acting on the body. The object holds zero acceleration since the net force acting is zero.

As the speed of the moving object increases, so does the drag force acting on it increases. It also depends on the substance it is passing through like for example air or water. At some speed, this drag force of resistance will equal the gravitational pull on the object. At this point, the object reached the constant terminal velocity.

The formula for Terminal Velocity:

\(V_{Terminal} = \sqrt{2 g h}\)

\(V_{Terminal}\)	Terminal Velocity
g	Acceleration due to gravity,
H	Height from the ground

Terminal velocity formula is used to calculate the terminal velocity as well as the acceleration due to gravity and height if any of these quantities are known. And terminal velocity is computed in meter per second i.e \(ms^{-1}\)

Solved Examples for Terminal Velocity Formula

Q.1: A man is at the height of 2000 m from the ground. What would be his terminal velocity using Terminal Velocity Formula?

Solution: Given,

Height h = 2000 m,

The terminal velocity formula is:

\(V_{Terminal} = \sqrt{2 g h}\)

\(= 197.98 m s^{-1}.\)

Thus terminal velocity will be \(197.98 ms^{-1}\)

Q.2: Determine the height of the body if its terminal velocity is \(100 m s^{-1}\)

Solution: Given parameters in the question are

Terminal velocity \(V_{terminal} = 100 m s^{-1},\)

The height can be computed by rearranging the formula as:

\(h = \frac {v^2} {2 g}\)

\(= \frac {100 ^2} { 2\times 9.8} =  \frac {10000}{ 19.6 }\)

= 510.204 m.

Height will be 510.204 meters.