Re: Bad textbooks (an example for the skeptical)

[Brian Whatcott <inet@INTELLISYS.NET>]

At 07:59 PM 2/16/02, you wrote:
> ...two problems both appear on the same page of the
> textbook (thankfully, in an appendix, not the main text).
>
> 1.   "A peach falls from a tree with an acceleration of 9.8 m/s^2 downward.
> The peach has a mass of 7.4 g. [Editorial comment: not a very big peach?
> But wait; here comes the good part!] With what force does the peach strike
> the ground?"
>
> 2.   "A person steps off a diving board and falls into a pool with an
> acceleration of 9.8 m/s^2, which causes the person to hit the water with a
> force of 637 N. What is the mass of the person?"
>
> Apparently neither the height of fall nor the duration of impact have any
> effect on the results.
> --MB


It is clear that the questions are modeling a rather special universe.
Taking question 2) first, if the height of fall is not given, we can suppose
 it is not material: This leads to the conclusion that one reaches terminal
velocity for any reasonable height of diving board there.
 If the impact force can be given, and related only to the mass of the person
then this drag force is (0.5 rho v^2 A Cd) and we suppose that v^2 A
 is proportional to mass. But mass could be modeled as proportional
to the volume of a cylinder of cross section A times height,
which leads us to deduce that here, the terminal velocity  v is
proportional to
sqrt(jumper's height)

This is the key to answering question 1), apparently:
a peach has a height sensibly equal to its cross sectional diameter.
Extending the deductions for prob 2) to prob 1) are now left as an exercise
for the student.


Brian Whatcott
  Altus OK                      Eureka!