# Momentum/Impulse- Calculating Average Force of Raindrops

So in the given time, the smaller drops would contribute a smaller force to the roof. Assuming the raindrop falls at a constant speed (likely not the case), then the total force acting on the roof is the product of the mass of the raindrop and the fall rate. This would be 48,768 kg * 10 m/s = 48,768 N.f

## 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"

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.

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.

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!