During heavy rain, a section of a mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0m 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 0.40km x 0.40km and that mud has a density of 1900kg/m3 (cubic meters). What is the mass of the mud sitting above 4.0m2 (squared meters)area of the valley floor?

Question

During heavy rain, a section of a mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0m 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 0.40km x 0.40km and that mud has a density of 1900kg/m3 (cubic meters). What is the mass of the mud sitting above 4.0m2 (squared meters)area of the valley floor?

Answer 1

The question makes no sense to me. what does above 4.0m^2 mean?

Answer 2

Thats what I'm confuse about, but that is what they have from the textbook... and the answer at the back of the back is 1.9x10^5 kg.

Answer 3

1) get initial volume (2500x800x2)

2) divide that volume by the surface area (400x400)
3) you have depth from equation 2
4) (4x4xdepthx1900)

Visualize it as this. You first find the cube. Then they want a cube inside that cube, the base being a 2x2 which is 4 meters squared.

If Depth is 25 then 25x4x1900 = 1.9x10^5kg

Answer 4

To find the mass of the mud sitting above a specific area of the valley floor, we will need to calculate the volume of the mud first, and then multiply it by the density to obtain the mass.

Given:
Width of the mountainside section (base of the mud slide) = 2.5 km = 2500 m
Height of the mountainside section (up along the slope) = 0.80 km = 800 m
Depth of the mud slide = 2.0 m
Area of the valley floor = 0.40 km x 0.40 km = 0.16 km^2 = 160,000 m^2
Density of mud = 1900 kg/m^3

To calculate the volume of the mud, we need to multiply the base area by the height, considering the depth:

Volume = base area x height
= (2.5 km x 0.80 km) x 2.0 m
= (2500 m x 800 m) x 2.0 m
= 4000000 m^2 x 2.0 m
= 8000000 m^3

So, the total volume of the mud is 8,000,000 m^3.

Now, to find the mass of the mud sitting above 4.0 m^2 area of the valley floor, we need to determine the volume of mud corresponding to that area by multiplying the area by the depth.

Volume of mud = Area x depth
= 4.0 m^2 x 2.0 m
= 8.0 m^3

Finally, we can calculate the mass of the mud by multiplying the volume by the density:

Mass = Volume x Density
= 8.0 m^3 x 1900 kg/m^3
= 15,200 kg

Therefore, the mass of the mud sitting above a 4.0 square meter area of the valley floor is 15,200 kg.