Question

A 90-kg skydiver jumps from a height of 6000 m above the ground, falling head-first (pike position). The area of the diver is 0.14 m2. The value for C is 1.0, and the density of air is 1.21 kg/m3. Determine the terminal velocity.

Answer 1

Answer:

102.097252061 m/s

Explanation:

F = Force

m = Mass = 90 kg

g = Acceleration due to gravity = 9.81 m/s² = a

C = Drag coefficient = 1

ρ = Density of air = 1.21 kg/m³

A = Surface area = 0.14 m²

v = Terminal velocity

Force is given by

F = ma

$F=\dfrac{1}{2}\rho CAv^2\\\Rightarrow ma=\dfrac{1}{2}\rho CAv^2\\\Rightarrow v=\sqrt{2\dfrac{ma}{\rho CA}}\\\Rightarrow v=\sqrt{2\dfrac{90\times 9.81}{1.21\times 1\times 0.14}}\\\Rightarrow v=102.097252061\ m/s$

Terminal velocity of the skydiver is 102.097252061 m/s