A recent estimate finds that approximately 800 meteorites with mass greater than 0.1 kg strike the surface of the Earth each day. If a house covers an area of roughly 100 m², then what is the probability that your house will be struck by a meteorite in your 100-year lifetime? Note that the radius of the Earth is 6,400 km. A) 1 in 1 *10⁴ B) 1 in 2 *10⁵ C) 1 in 4* 10⁶ D) 1 in 6 *10⁷ E) 1 in 8 * 10⁸

Question

Quizplus · Accepted Answer

First, we need to calculate the area of the Earth that is being targeted by the meteorites, which can be approximated as a circle with a radius of 6,400 km (the radius of the Earth).

Area of circle = πr^2 = π(6,400 km)^2 = 1.29 x 10^8 km^2

Convert this to square meters: 
1.29 x 10^8 km^2 x (1,000 m/km)^2 = 1.29 x 10^14 m^2

Assuming that each meteorite has an equal chance of hitting any point on the Earth's surface, the probability of a single meteorite hitting a particular 100 m x 100 m area (i.e. a house) is:

(100 m x 100 m)/(1.29 x 10^14 m^2) ≈ 7.7 x 10^-12

To calculate the probability of a house being hit by at least one meteorite in a 100-year lifetime, we need to multiply the daily rate of meteorite impacts by the number of days in a century:

800 meteorites/day x 365.25 days/year x 100 years = 2.92 x 10^7 meteorites

Using the probability of a single meteorite hitting a house that we calculated above, we can calculate the probability of a house being hit by at least one meteorite over a 100-year lifetime:

1 - (1 - 7.7 x 10^-12)^2.92 x 10^7 ≈ 1.54 x 10^-4

This is equivalent to a probability of approximately 1 in 6.5 million, or 1 in 2 x 10^7. Therefore, the answer is choice B.

A Recent Estimate Finds That Approximately 800 Meteorites with Mass