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

Answer:

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

$W=F_L$

$F_L=\frac{c_DA\rho v^2}{2}$

W=mg

$80\times 9.81=\frac{0.5\times \frac{\pi d^2}{4}\times 1.35\times 25^2}{2}$

$784.8=165.691\times d^2$

d=2.17 m