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Classical Mechanics

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Drag Force and Terminal Velocity: Changing Atmosphere Density

CLMECH-LNVYJB

The density of Earth's atmosphere decreases with altitude such that the density at an altitude of 10,000 m is only $33\%$ of the density at sea level. However, the acceleration due to gravity is not significantly different at 10,000 m from its value at sea level.

If a skydiver jumps from an airplane at an altitude of 10,000 m, how will her terminal velocity just before landing compare to her terminal velocity at 10,000 m (assuming her cross-sectional area remains constant)?

The air resistance acting on the skydiver has a magnitude of $\left |F_{drag}\right | = \frac{1}{2}c\rho Av^2$, where c is a constant.

A

Her terminal velocity before landing is $33\%$ of her terminal velocity at 10,000 m.

B

Her terminal velocity before landing is $57\%$ of her terminal velocity at 10,000 m.

C

Her terminal velocity before landing is $130\%$ of her terminal velocity at 10,000 m.

D

Her terminal velocity before landing is $170\%$ of her terminal velocity at 10,000 m.