Question

An 80 kg man descends to the ground from an aeroplane using a parachute. If the drag coefficient of the parachute is 0.5 and the density of air is 1.35 kg/m3, calculate the required diameter of the parachute so that the man descends with a velocity of 25 m/s.

Answer 1

Explanation:2.17 m

Given

Mass of man=80 kg

drag coefficient
`(c_D)=0.5`

Density of air
`=1.35 kg/m^3`

Required descend velocity(v)=25 m/s

Let d be the diameter of Parachute

In this case Drag force will oppose weight of man so that net force is zero and there is a constant velocity of descend

`W=F_L`

`F_L=(c_DA\rho v^2)/(2)`

W=mg

`80* 9.81=(0.5* (\pi d^2)/(4)* 1.35* 25^2)/(2)`

`784.8=165.691* d^2`

d=2.17 m