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If one micrometeorite (a sphere with a diameter of 1.0 ✕ 10-6) struck each square meter of the moon each second, it would take many years to cover the moon with micrometeorites to a depth of 1.9 m. consider a cubic box, 1.9 m on a side, on the moon. estimate how long it would take to completely fill the box with micrometeorites if one micrometeorite landed in the box each second.

Respuesta :

area of the cube is given by

[tex]A = 1.9 * 1.9[/tex]

[tex]A = 3.61 m^2[/tex]

now the area covered by one micrometeorite

[tex]A' = (1 * 10^{-6})^2[/tex]

[tex]A' = 1* 10^{-12} m^2[/tex]

now we will find the time to cover this area

[tex]t = \frac{A}{A'}[/tex]

[tex]t = \frac{3.61}{1* 10^{-12}}[/tex]

[tex] t = 3.61 * 10^{12}s[/tex]

now we need to fill the whole cube

so the height required to be filled

[tex]T = \frac{1.9}{1* 10^{-6} * 3.61 * 10^{12}[/tex]

[tex]T = 6.86 * 10^{18} s[/tex]

[tex]T = 2.2 * 10^{11} years[/tex]

so above time is required

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