Momentum/Impulse- Calculating Average Force of Raindrops

[MadTay]

Homework Statement

The problem says:
"A record rainstorm produced 304.8 mm (approximately 1 ft)
of rain in 42 min. Estimate the average force that the rain exerted
on the roof of a house that measures 10 m * 16 m. Indicate
any assumptions you made. (Note: density of water is 1000 kg/m³"

Homework Equations

Volume= lwh
Favg=ΔP/ΔT
ΔP= mΔV

The Attempt at a Solution

I determined the mass of the rain that fell in the 42 minute/2520 second interval to be 48,768kg and the mass of rain to fall in one second to be 19.35kg.
From there I am absolutely at a loss of what to do to figure out the average force. Assuming that the final velocity of the rain is 0, I'm thinking that I need the initial velocity of the rain in order to figure out the change in momentum.
The answer itself isn't a problem, as I was given a key, but I'm not sure if I should use the mass of all of the rain and 2520 seconds as Δt or use 19.35kg and 1 second as Δt. I'm just really not sure where to go after calculating the masses of the amounts of rain.
The key says the answer is 2x10^-4 N, but I can't figure out how to get to that answer.

 

[Bystander]

thinking that I need the initial velocity of the rain

Which is absolutely correct. Large raindrops in a torrential downpour might be moving 10 m/s. That and the mass rate you've calculated eventually give you a number that's for force ~ 2, but the order of magnitude is off by a factor of 6. Whoever solved it for the answer key probably used 10 m/s for the fall rate, but mixed grams and tons.

 

[MadTay]

Which is absolutely correct. Large raindrops in a torrential downpour might be moving 10 m/s. That and the mass rate you've calculated eventually give you a number that's for force ~ 2, but the order of magnitude is off by a factor of 6. Whoever solved it for the answer key probably used 10 m/s for the fall rate, but mixed grams and tons.

Whew! Glad to know it wasn't a lack of knowledge on my part that was stopping me from getting to that answer. Thank you very much for your help!

 

[DEvens]

The 10 m/s seems reasonable.

http://wxguys.ssec.wisc.edu/2013/09/10/how-fast-do-raindrops-fall/

The smaller drops presumably make up a small fraction of the total mass of water.