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Akimi4
3 months ago
14

The air is less dense at higher elevations, so skydivers reach a high terminal speed. The highest recorded speed for a skydiver

was achieved in a jump from a height of 39,000 m. At this elevation, the density of the air is only 4.3% of the surface density of air at 20∘C. Estimate the terminal speed of a skydiver at this elevation. Suppose the mass of the skydiver is 90 kg and the cross section area of the skydiver is 0.72 m2. You could consider the diver as a cylinder traveling sideways for this problem.
Physics
1 answer:
serg [3.5K]3 months ago
5 0

Answer:

The terminal velocity v_t= 202.96 m/s, approximately 203 m/s.

Explanation:

The formula for terminal velocity is given by

v_t= \sqrt{\frac{2mg}{\rho AC_d} }

Here, C_d represents the drag coefficient for the cylindrical shape, which is 1.15.

The air's surface density at 20°C is

ρ_surface = 1.2041 kg/m³.

At an altitude of 39,000 m, the air density is calculated as

ρ = 4.3/100 × 39000 = 0.05177 kg/m³.

Substituting these values back into the formula yields

v_t= \sqrt{\frac{2\times90\times9.81}{0.05177\times0.72\times1.15} }

The found terminal velocity v_t is 202.96 m/s, or roughly 203 m/s.

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