Where Should the Safety Net be Placed on a Skyscraper to Catch Falling Debris?

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Homework Statement

An architect who is building a skyscraper comes to see you. The architect wishes to
place a safety net on the skyscraper, to prevent damage or injury should any of the
building's decorative features be dislodged by wind or other forces. What advice can
you give her on how far down the building to place the net (the farther down the better,
for various practical reasons), assuming: any falling debris will fall from rest, subject to
an air resistance proportional to its velocity; the safety net will catch the debris as long
as its speed is below n times its terminal velocity for some xed n 2 (0; 1)? Note that
your answer can depend on certain constants.

Homework Equations

The Attempt at a Solution

velocity of debris v(t)= ce^(-rt/m) - mg/r has to be less that -nmg/r where r is the location of the debris ie (top of buildin). m = mass of debris and g is 9.8. t= time. these assumptions about m and r may be incorrect so please correct them if you think i am wrong.

 

[jbsteele]

the architect should place the net at a position such that velocity of debris at that position is below -nmg/r.