Question

A paratrooper and his 8-m-diameter parachute weigh 1000 N. Taking the average air density to be 1.2 kg/m3, determine the terminal velocity of the paratrooper.Take the drag coefficient of the parachute as CD

Answer 1

Answer:
`v_(T)` = 4.35 m/s

Explanation: Drag Force opposes the motion of an object and depends on shape, size, velocity of the object or person and the fluid it is in.

Terminal velocity occurs when gravitational force and drag force are equal, which gives a net force and acceleration of zero. At that moment, velocity is constant and called terminal.

Terminal velocity is found by the following formula:

`v_(T)=\sqrt{(2mg)/(\rho.CA) }`

ρ is density of the fluid

C is drag coefficient

A is area of the object in which forces are acting

The paratrooper and his parachute weighs 1000N, so this means

mg = 1000

Drag coefficient of a parachute is an average of C = 1.75

A parachute is half an sphere. So, area is

`A=0.5[4.\pi.r^(2)]`

`A=2.\pi.4^(2)`

A = 16π m²

Substituing:

`v_(T)=\sqrt{(2.1000)/(1.2.1.75.16.\pi) }`

`v_(T)=\sqrt{(2000)/(105.557) }`

`v_(T)` = 4.35

The terminal velocity of the paratrooper is 4.35m/s