If a rainstorm drops 4 cm of rain over an area of 12 km- in the period of 2 hours, what is the momentum (in kg - m/s) of the rain that falls in nine seconds? Assume the terminal velocity of a raindrop is 10 m/s. (Enter the magnitude. The density of water is 1,000 kg/m. 0.35 x kg m/s
If a rainstorm drops 4 cm of rain over an area of 12 km- in the period of 2 hours, what is the momentum (in kg - m/s) of the rain that falls in nine seconds? Assume the terminal velocity of a raindrop is 10 m/s. (Enter the magnitude. The density of water is 1,000 kg/m. 0.35 x kg m/s
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![**Problem Statement:**
If a rainstorm drops 4 cm of rain over an area of 12 km² in a period of 2 hours, what is the momentum (in kg·m/s) of the rain that falls in nine seconds? Assume the terminal velocity of a raindrop is 10 m/s. Enter the magnitude. The density of water is 1,000 kg/m³.
**Input Field:**
The answer input field contains the value: 0.35 kg·m/s.
**Explanation:**
To calculate the momentum of the rain, use the formula for momentum:
\[ \text{Momentum} = \text{mass} \times \text{velocity} \]
1. **Volume Calculation:**
- Convert the rain depth from centimeters to meters: 4 cm = 0.04 m.
- Calculate the volume of rain using area and depth: \( \text{Volume} = \text{Area} \times \text{Depth} = 12 \times 10^6 \, \text{m}^2 \times 0.04 \, \text{m} = 480,000 \, \text{m}^3 \).
2. **Mass Calculation:**
- Find the mass using the volume and density of water:
\[ \text{Mass} = \text{Volume} \times \text{Density} = 480,000 \, \text{m}^3 \times 1,000 \, \text{kg/m}^3 = 480,000,000 \, \text{kg} \]
3. **Rate of Rainfall:**
- Determine the total duration in seconds for the volume of rain: 2 hours = 7200 seconds.
- Calculate the volume that falls in nine seconds:
\[ \text{Volume in 9 seconds} = \frac{480,000 \, \text{m}^3}{7200 \, \text{s}} \times 9 \, \text{s} \approx 600 \, \text{m}^3 \]
4. **Mass in 9 seconds:**
- Find the mass of rain in nine seconds:
\[ \text{Mass in 9 seconds} = 600 \, \text{m}^3 \times 1,000 \, \text](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75758824-d9ac-45ff-8935-fa266cdc3747%2F256e71df-67b9-424d-847c-c52878df2295%2Fypq7fj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If a rainstorm drops 4 cm of rain over an area of 12 km² in a period of 2 hours, what is the momentum (in kg·m/s) of the rain that falls in nine seconds? Assume the terminal velocity of a raindrop is 10 m/s. Enter the magnitude. The density of water is 1,000 kg/m³.
**Input Field:**
The answer input field contains the value: 0.35 kg·m/s.
**Explanation:**
To calculate the momentum of the rain, use the formula for momentum:
\[ \text{Momentum} = \text{mass} \times \text{velocity} \]
1. **Volume Calculation:**
- Convert the rain depth from centimeters to meters: 4 cm = 0.04 m.
- Calculate the volume of rain using area and depth: \( \text{Volume} = \text{Area} \times \text{Depth} = 12 \times 10^6 \, \text{m}^2 \times 0.04 \, \text{m} = 480,000 \, \text{m}^3 \).
2. **Mass Calculation:**
- Find the mass using the volume and density of water:
\[ \text{Mass} = \text{Volume} \times \text{Density} = 480,000 \, \text{m}^3 \times 1,000 \, \text{kg/m}^3 = 480,000,000 \, \text{kg} \]
3. **Rate of Rainfall:**
- Determine the total duration in seconds for the volume of rain: 2 hours = 7200 seconds.
- Calculate the volume that falls in nine seconds:
\[ \text{Volume in 9 seconds} = \frac{480,000 \, \text{m}^3}{7200 \, \text{s}} \times 9 \, \text{s} \approx 600 \, \text{m}^3 \]
4. **Mass in 9 seconds:**
- Find the mass of rain in nine seconds:
\[ \text{Mass in 9 seconds} = 600 \, \text{m}^3 \times 1,000 \, \text
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