During heavy rain, a section of a mountainside measuring 5.4 km horizontally (perpendicular to the slope) 0.80 km up along the slope, and 2.1 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 1.1 km x 1.1 km and that the mass of a cubic meter of mud is 1900 kg. What is the mass of the mud sitting above a 5.7 m2 area of the valley floor?

Question

During heavy rain, a section of a mountainside measuring 5.4 km horizontally (perpendicular to the slope) 0.80 km up along the slope, and 2.1 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 1.1 km x 1.1 km and that the mass of a cubic meter of mud is 1900 kg. What is the mass of the mud sitting above a 5.7 m2 area of the valley floor?

Answer 1

To find the mass of the mud sitting above a 5.7 m² area of the valley floor, we need to calculate the volume of the mud and then multiply it by the mass per unit volume.

1. Start by finding the volume of the mud. We know that the section of the mountainside measures 5.4 km horizontally (perpendicular to the slope), 0.80 km up along the slope, and 2.1 m deep. We need to convert these measurements to the same units before we can calculate the volume.

- Convert 5.4 km to meters: 5.4 km * 1000 m/km = 5400 m
- Convert 0.80 km to meters: 0.80 km * 1000 m/km = 800 m

2. Now we can calculate the volume of the mud. Since the section of the mountainside is a rectangular solid, the volume is given by multiplying the length, width, and height.

Volume of mud = length * width * height = 5400 m * 800 m * 2.1 m = 9072000 m³

3. Next, we need to calculate the mass of the mud by multiplying the volume by the mass per unit volume. We are given that the mass of a cubic meter of mud is 1900 kg.

Mass of mud = Volume of mud * Mass per unit volume = 9072000 m³ * 1900 kg/m³ = 1.7228e+10 kg

4. Finally, we need to find the mass of the mud sitting above a 5.7 m² area of the valley floor. Since the mud is uniformly distributed over a 1.1 km x 1.1 km area, we can find the mass of the mud per unit area and then multiply it by the given area.

Mass per unit area = Mass of mud / Area of valley floor = 1.7228e+10 kg / (1.1 km * 1.1 km) = 1.622e+7 kg/m²

Mass above 5.7 m² area = Mass per unit area * Area = 1.622e+7 kg/m² * 5.7 m² = 9.242e+7 kg

Therefore, the mass of the mud sitting above a 5.7 m² area of the valley floor is approximately 9.242e+7 kg.

500

To find the mass of the mud sitting above a 5.7 m² area of the valley floor, we need to calculate the volume of the mud and then multiply it by the mass per unit volume.