Answered

During heavy rain, a section of a mountainside measuring 2.3 km horizontally (perpendicular to the slope), 0.75 km up along the slope, and 1.4 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.52 km x 0.52 km and that the mass of a cubic meter of mud is 1900 kg. What is the mass of the mud sitting above a 5.5 m2 area of the valley floor?

Answer :

boffeemadrid

Answer:

93328 kg

Explanation:

[tex]\rho[/tex] = Density of mud = 1900 kg/m³

Volume of the cuboid is given by

[tex]V=2300\times 750\times 1.4\\\Rightarrow V=2415000\ m^3[/tex]

Volume is also given by

[tex]V=Al\\\Rightarrow l=\dfrac{V}{A}\\\Rightarrow l=\dfrac{2415000}{520\times 520}\\\Rightarrow l=8.9312\ m[/tex]

The length of the cuboid is 0.89312 m

For the small volume

[tex]V_a=al\\\Rightarrow V_a=5.5\times 8.9312\\\Rightarrow V_a=49.12\ m^3[/tex]

Mass is given by

[tex]m=\rho V_a\\\Rightarrow m=1900\times 49.12\\\Rightarrow m=93328\ kg[/tex]

The mass of the mud is 93328 kg

Other Questions