# A RAINY problem

1. Mar 10, 2008

### puneeth

1. The problem statement, all variables and given/known data
Suppose it is raining at a constant rate (at any instant the number of raindrops in a given volume of space will be constant) . there is no wind and rain falls vertically. two persons of same size (height, stoutness etc) set out to travel a fixed distance say d meters in a straight path one on a bicycle moving at const. speed of 10 Km/hr and other on a bike moving with 20 Km/hr. who gets more wet?
N.B : they travel WITHOUT stopping.

2. Relevant equations
distance/time = speed.
volume swept during journey = surface area x speed

3. The attempt at a solution
when a person moves in space the raindrops hitting him are those which should have been present in the space which he occupies at that particular instant. suppose that the person is photographed at a particular instant, the raindrops which hit him at that instant are those which were present in tthe volume he occupies in that instant. since he is in a state of continuous motion the drops on, beside before, or behind him do not affect him.
also since rain falls at a constant rate the number of raindrops striking a person during his journey should then equal the volume swept by him x no. of rain drops per unit volume.
since both are of the same size and move same distances the volumes swept are equal.
then it leads to the conclusion thar both are wetted to the same extent.
this conclusion seems to oppose common sense, for we run to our destinations rather than walking when it rains - but in both cases we are wetted to the same extent!
hence I doubt the validity of the arguement.

2. Mar 10, 2008

### Oerg

the flaw in your argument is that you have not considdered time at all. Rememeber that the number of raindrops falling on a person is a function of time. This means that the only factor determining how wet a person is going to get if rate of rainfall is the same is time.

3. Mar 10, 2008

### puneeth

the rate of rainfall is same in the ground frame of reference.... but a fast moving person sweeps the same volume... may be in lesser time, but the number of rain drops he hits in the interim period is the drops whose space he occupied during his journey - which is completely independent of time. i still feel it depends only on the distance.
the following picturization may be helpful in correctly understanding my arguement -
since the number of rain drops is same in a given volume of space at any instant - let us look at the rain and FREEZE our view at an instant. the rain drops now hang at their respective places without falling ( both the systems are similar - the number of drops is still the same in any given volume). Now send the motorcyclist - he hits all the drops located in the volume his body sweeps. there are no drops behind him - but in the original model the drops reappeared due to continuity of the rain. but that is irrelevent to the motorcyclist or how wet he gets. the number of drops hitting him now appears to be ONLY a function of the volume he sweeps - which is dependent in turn on the distance and his dimensions - NOT on time! thus the cyclist whould be wet to the same degree!
may be this argument is more clear.... please express your views .

4. Mar 10, 2008

### Dick

If he stands still he will collect the same amount of raindrops on his vertical cross section as when he is moving. If he stands still he will collect no raindrops on his horizontal cross section. If he is moving he will. He is wetter if he moves.

5. Mar 11, 2008

### puneeth

both move in this case - who gets more wet? even though the rate of getting wet is more in case of motor cyclist os more he spends lesser time in rain and the cyclist spends more time in rain though the rate of getting wet is less. hence the argument that both get wet to the same extent seems more probable. time does not seem to play any role here.

6. Mar 11, 2008