Skydiver-Speed problem

Question

A skydiver with a mass of 47 kg has a parachute with an area of A=44 m^2. After opening the parachute and reaching the terminal speed with the parachute, how fast does she descend through the air?

Answer 1

Let

m = 47 kg be the mass of the skydiver,

A = 44 m² be the area of the parachute,

ρ = 1.229 kg/m³ be the density of air,

C = 1.75 be the drag coefficient of the parachute,

g = 9.81 m/s² be gravitational acceleration,

v be the velocity of the fall.

When the skydiver is falling with velocity v, the parachute causes an upward drag force

CρAv²/2

The skydiver reaches terminal velocity when the drag force becomes equal to the weight

mg

That is, v is the termival velocity when

CρAv²/2 = mg

v = √(2mg/CρA) = √(2×47×9.81/(1.75×1.229×44)) = 3.1 m/s