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Salient: Victoria University Students' Paper. Vol. 28, No. 11. 1965.

Mr X's Column

Mr X's Column

Column was mulling over a problem the other day. He had just run from Hunter Building to Sub through a particularly heavy shower of rain.

Does one get wetter running through rain or walking through it? Was lost in contemplation of this when I bumped into two Physics Honours students engaged in the self-same problem.

They have deduced the optimum velocity at which one must travel between Sub and Hunter Building during steady, non-relatavistic, vertical rain, assuming one desires not to get wet.

Consider a right rectangular man:

A. is his horizontal cross-section.

B. „ „ vertical cross-section.

v. „ „ linear velocity.

V. the vertical velocity of the rain.

It can be shown that the mass M. of water collected by the man in unit time is:

M=K (sin X + B sin X).

(v2 + V2)½

where—X=tan-1 (V/v)

K is the so-called Spling's constant, which depends on the rainwater flux, and on the sobriety of the man. Hence it can be shown that the total mass collected is given by:

M (total)=K.D. (A sin X + B sin X).

(sec X)=K.D (AV/v + B)

where D. is the distance to be covered.

After extensive numerical computation by computer, this expression was found to represent a hyperbola which reached assymptotically a minimum mass M(min) given by:

M(min)=K.D.B.

for v.=999,999,999.999 km/sec.

(to 12 decimal places)

To summarise for our non-scientific readers, the optimum method to cross from Sub to Hunter Building in steady, non-relatavistic, vertical rain is to run linearly in the positive direction at infinite speed. This result can be applied to the reverse journey by an appropriate change of sign.

Apparently some other notes on the effect of non-relatavistic, vertical rain incident on a spherical man were rendered illegible by the self-same shower of rain. A loss to some of the more rotund members of the campus. I am indebted to R.F. and G.P. for this information; and I think it refutes the popular conception of the lack of practical research by the Physics Department.

Some puzzles for the mathematically minded:—

1. Decimal coinage seems to be the thing these days so try this: What is the minimum number of coins required to express any value of 1 to 100 cents in no more than two coins, e.g. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90 cents. A total of 18. Column has an answer that is smaller.

Answer next issue