2. Extinction-Level Event. Buried underneath Mexico\'s Yucatán Peninsula is the

Question

2. Extinction-Level Event. Buried underneath Mexico's Yucatán Peninsula is the Chicxulub crater, more than 180 km in diameter. The impact that created this crater released an estimated energy equivalent to 100 Teratons of TNT (4.2×1023 J), and has been implicated in causing the extinction of the dinosaurs 65 million years ago Let's assume that the object responsible for this event was a sphere of rock with density of 3 g/cm3 (typical for asteroids and comets), and it entered Earth's atmosphere at a speed of 30,000 m/s (comparable to Earth's orbital speed around the Sun). Assume also that atmospheric drag did not slow the object down significantly before impact (see part b) a. What was the estimated mass (in kg) and diameter (in m) of the object? Show all of your work! b. Given that Earth's atmosphere is 100 km thick, and assuming the object fell straight down through the atmosphere, calculate the fraction of its final kinetic energy the object lost to the atmospheric drag force. Use 0.7 for the drag coefficient and 1 kg/m3 for the density of Earth's atmosphere c. The energy lost to drag was dissipated as heat. Calculate the power in Gigawatts produced by the object as it fell. (Because most of this heat is radiated as light, the object would have appeared as a very bright meteor, or fireball in the sky.) Hint: Use the energy lost to drag and the time it took the object to fall through the atmosphere to calculate the power (the energy dissipated perunittime)

Explanation / Answer

a)

E = 4.2*10^23

Density = 3000 kg/m3

Velocity = 30000 m/s

So, 1/2mv2 = E

M = 2E/v2

M = 9.333*10^14 kg

Density = mass/volume

Volume = 4/3(pi)(R^3)

R = 4.204*10^3 m

Diameter = 8408.0044 m

b)

The fraction = ½ CdAv2

C = drag coefficient = 0.7

A = Cross sectional area = (pi)(r2)

V = Velocity = 30000 m/s

D = Density of earth = 1 kg/m3

So The Fraction = 1.94*10^7 j

C)

Power = Drag force * velocity

P = 582 Gigawatts

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