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#### Definition Of Terminal Velocity And State Its Formula

Referencing Styles : Harvard | Pages : 1

### Terminal Velocity

Whenever an object falls, the gravitational force causes the object to increase its speed as it was predicted by Isaac Newton. As the speed of the object gradually increases the force of air drag increases eventually. The air drag force is equal to that of the gravitational force. At that time there is no force which is acted on the object. In this case, if the force is balanced precisely, the object will not speed up further though it will slow down its speed and the falling will be continued in a constant velocity. This is known as the terminal velocity.

As the force of air drag is depended highly on the size of the object and the shape of the object, the objects which have an area of the large surface will have a terminal velocity that is comparatively lower than the objects which have the smaller surface area. The object weight even effects on the force of air drag over the object which results in the terminal velocity.

### Calculation of terminal velocity

Three different ways are used to calculate the value for the terminal velocity. They are as follows:

1. Solving for the terminal velocity.

V = the square root of ((2*m*g)/(p*A*C)). The following values are plugged into the formula in case of solving the terminal velocity (v)

• M = mass of the object which is falling.
• G = the acceleration caused due to gravity. On the earth, this has an approximate value of 9.8 meters per second.
• P = the density of the fluid through which the object is falling.
• A = the area which is projected for the object. This means the object area in which if projected on a plane surface which is perpendicular to that of the direction in which the object is moving.
• C = this is the drag coefficient. This is the number that is dependent on the shape of the respective object. In this case, the shape is more streamlined, the coefficient is also lower. The coefficient is approximately considered.
1. Find the Gravitational force

In this method there are following steps that are to be followed:

a) Find the mass of the respective object. This is measured in the unit of a gram or else kilograms.

• If the imperial systems are used, it is to be remembered that the pound is not included in the unit for mass or in case of any force. The mass unit is an imperial system is pound-mass which is under the gravitational force over a surface on the earth which will experience a force of around 32 pound-force.

b) Acceleration caused due to the gravity present on the earth.

• This is closer to the earth that encounters resistance in the air. The acceleration is around 9.8 meters per second squared or else it is 32feet per second squared.

c) Calculate the gravity's downward force. The force by which the object which is falling is pulled downwards that is equal to the mass time acceleration due to the gravity of the objects. F = MA. This is the number which is multiplied by 2 and this goes on top of the formula of the terminal velocity.

• In the case of the imperial system, this is defined as the lbf of an object, this is the very common number and it is called weight. This is the mass in lbm times which is squared with 32 feet per second. In the metric system, the mass is the force calculated in the unit of grams which is termed as 9.8 meters per Second Square.

3) Determination of the drag force

In this method there are the following steps that are discussed below:

a) Get the medium density.

b) Estimation of the drag coefficient of the object.

c) Calculation of the area of the object that is projected.

d) Getting the drag force that opposes the downward gravitational pull.

### Calculation Example

Example 1

A man is at the height of 2000 m from the ground. What would be his terminal velocity?

Solution

Given:

Height h = 2000 m,

The terminal velocity formula is given by

V terminal = √2×9.8 ×2000

= √39200

= 197.98 m/s.

Example 2

Determine the height of the body if its terminal velocity is 100 m/s.

Solution

Given:

Terminal velocity V terminal = 100 m/s,

The height is given by

h = v2terminal / 2g

= 10000 / 9.8 x 2

= 510.204 m.

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