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The terminal velocity of a person falling in air depends upon the weight and the area of the person facing the fluid. Find the terminal velocity (in meters per second and kilometers per hour) of an 84.0 kg skydiver falling in a pike (headfirst) position with a surface area of 0.160 m2. (Assume that the density of air is 1.21 kg/m3 and the drag coefficient of a skydiver in a pike position is 0.7.)

Respuesta :

Answer:

110.27 m/s or 396.972 km/h

Explanation:

F = Force

m = Mass = 84 kg

g = Acceleration due to gravity = 9.81 m/s²

C = Drag coefficient = 0.7

ρ = Density of air = 1.21 kg/m³

A = Surface area = 0.16 m²

v = Terminal velocity

F = ma

[tex]F=\frac{1}{2}\rho CAv^2\\\Rightarrow ma=\frac{1}{2}\rho CAv^2\\\Rightarrow v=\sqrt{2\frac{ma}{\rho CA}}\\\Rightarrow v=\sqrt{2\frac{84\times 9.81}{1.21\times 0.7\times 0.16}}\\\Rightarrow v=110.27\ m/s[/tex]

Converting to km/h

[tex]\frac{110.27}{1000}\times 3600=396.972\ km/h[/tex]

Terminal velocity of the skydiver is 110.27 m/s or 396.972 km/h

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