A severe thunderstorm dumped 2.0 in of rain in 30 min on a town of area 50 km^2. What mass of water (in kg) fell on the town? One cubic meter of water has a mass of 103 kg.
To find the mass of water that fell on the town, we need to calculate the volume of water that was deposited and then multiply it by the mass of one cubic meter of water.
Given:
- The amount of rain that fell is 2.0 inches.
- The time it took for the rainfall is 30 minutes.
- The area of the town is 50 km^2.
First, let's convert the rainfall from inches to meters. 1 inch is equal to 0.0254 meters, so we can calculate the rainfall as follows:
Rainfall = 2.0 inches * 0.0254 meters/inch = 0.0508 meters
Next, we need to determine the volume of water that fell on the town. The volume of water can be calculated by multiplying the area of the town by the rainfall:
Volume = Area * Rainfall
The area of the town is given as 50 km^2, but we need to convert it to square meters to match the unit of the rainfall:
Area = 50 km^2 * (1000 m/km)^2 = 50,000,000 m^2
Now we can calculate the volume of water:
Volume = 50,000,000 m^2 * 0.0508 meters = 2,540,000 cubic meters
Finally, we can calculate the mass of water in kilograms. Given that one cubic meter of water has a mass of 103 kg:
Mass = Volume * Mass of one cubic meter of water
Mass = 2,540,000 cubic meters * 103 kg/cubic meter = 261,820,000 kg
Therefore, the mass of water that fell on the town is 261,820,000 kg.