Respuesta :
Answer:
8.30 Million years        Â
Explanation:
Assuming that --
In one day, the moon's surface is hit by the number of micrometeorites
= 25 million                                                                               = 25000000
To erase a footprint, the number of impacts needed are  = 20
It is given that area of footprint = 300 cm²
We know that surface area of the Moon is = 37.93 Million Km²
                                   = [tex]37.93\times 10^{16} cm^{2}[/tex]
Therefore, using above information, we get
No. of impacts on the moon per day per cm² is = [tex]\frac{25000000}{37.93\times 10^{16}}[/tex]
∴ No. of impacts on area of a foot print (300 cm²) per day will be,
= [tex]\frac{25000000}{37.93\times 10^{16}} \times 300[/tex]
= [tex]6.59\times 10^{-9}[/tex]
Now as assumed there must be 20 impacts on the footprint's area to erase the footprint
Time taken for [tex]6.59\times 10^{-9}[/tex] impacts = 1 Day
∴ Time taken for 1 impact is given by
= [tex]\frac{1}{6.59\times 10^{-9}}[/tex] days
Therefore, the time taken for 20 impacts will be
= [tex]\frac{1}{6.59\times 10^{-9}}\times 20[/tex] days
= [tex]3.03\times 10^{9}\\[/tex]
= [tex]\frac{3.03\times 10^{9}}{365}[/tex]
= [tex]8.30\times 10^{6}[/tex] years
Hence, it would take 8.30 million years for the footprint to be erased.
