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Assume there is a rainstorm, and the rain falling over the entire subject area is perfectly, uniformly distributed. Now assume there are two identical cars in this area. One is standing still, and one is traveling (at any rate, it doesn't matter).

In theory, does one get struck by more water than the other? I understand that the velocity at which the raindrops strike the moving car will be higher. But because the surface area of the vehicles is identical and the rain is uniformly distributed, shouldn't each get hit by the same amount of water at any given moment or over any span of time?

My intuition is pulling me in all sorts of different directions on this question.

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This was covered in reasonable enough detail in this video youtube.com/watch?v=3MqYE2UuN24 which should help you answer your question. –  Brandon Enright Apr 20 '13 at 0:09
What shape is the car? I think this is a crucial piece of data nobody mentions. –  Peter Shor Apr 20 '13 at 1:48
Possible duplicate: physics.stackexchange.com/q/19499/11062 –  Waffle's Crazy Peanut Apr 20 '13 at 2:14
This was marked as a duplicate, but it's not, as I've explained in a comment on the other question. –  Ben Crowell Apr 20 '13 at 16:11
Hi @BenCrowell: If you think it's not, you can always use the reopen vote (since you have the privilege) so that it comes under the review queue. Or the other way, you can always flag it for mod attention ;-) –  Waffle's Crazy Peanut Apr 20 '13 at 16:15
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marked as duplicate by Waffle's Crazy Peanut, Manishearth Apr 20 '13 at 11:27


3 Answers

up vote 6 down vote accepted

My understanding of the question is that it's about minimizing the rate at which rain hits the car. That makes it different from this question, which assumes you want to minimize the total amount of water that hits you before you get to a certain destination.

First let's assume the rain is perpendicular to the road and the car is a sphere. Then by the following argument, more rain hits the moving car.

We have $\mathbf{v}_{cr}=\mathbf{v}_{ce}+\mathbf{v}_{er}$, where $\mathbf{v}_{cr}$ is the car's velocity relative to the rain, $\mathbf{v}_{ce}$ is the car's velocity relative to the earth, and $\mathbf{v}_{er}$ is the earth's velocity relative to the rain. Let the car have cross-sectional area $A$. In the rain's frame of reference, the car is moving at $\mathbf{v}_{cr}$, and in time $t$ it sweeps out a volume $V=At|\mathbf{v}_{cr}|$. This volume is maximized by maximizing $|\mathbf{v}_{cr}|$, and if $\mathbf{v}_{ce}$ is perpendicular to $\mathbf{v}_{er}$, then this is always maximized by mazimizing $|\mathbf{v}_{ce}|$.

In reality, the car isn't a sphere, so the cross-sectional area $A$ presented to the rain is a variable. In some cases, this could allow the car to hit less rain while moving. As an unrealistic example, suppose the car is a pancake tilted at an angle of 45 degrees, and the rain is falling at 10 km/hr. Then the car can minimize how much rain hits it by driving at 10 km/hr.

If the rain isn't perpendicular to the road, but the car is a sphere, then $|\mathbf{v}_{cr}|$ may be minimized for some nonzero value of $\mathbf{v}_{ce}$.

These examples show that in general, the result depends on both the shape of the car and the angle of the rain with respect to the road.

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You will hit more rain if you move faster with respect to the amount of time, with the assumption that rains are falling Perpendicularly

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Both the car should get same amount of rain.

if you keep 2 buckets(one 10"dia & another 20" dia)in the rain, irrespective of diameter diff in bucket, you will get same height of water in it. this gives us a conclusion that, flow rate of rainfall is uniform at any given time.

flow rate is volume/time.so this is time dependent. if the car is moving or stationary, the time it is in the rain determins how much it gets wet.

imagine you keep 10 polls with equal distance of 1meter.you are firing a bullet from 10 gun straight to pole at every 1sec.in 1sec pole will get shot 1time.

now you take one gun and move the gun firing in every 1 sec, still you will shoot 10 pole once in every 1 sec.

same way, whether you move car or not. the rain will fall at same rate everywhere. its velocity cant change

while in motion, due to turbulence, the rain fall cannot be same everywhere in the car, back side of the car will not get much wet, because, the wind carries the rain drops away and makes it non uniform. but if you ignore this fact/assume its heavy rain and water droplets are huge, then it should be same for stationary car as well as a moving car.

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