Question #360e8

1 Answer
Alan P.
Feb 27, 2015

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To simplify calculations all foot or foot-inch values have been converted to number of "half-feet"

Based on similar triangles we can see that
the shadow length, #s(t)#, is related to the walked distance, #w(t)#. by the ratios
#(s(t))/11 = (s(t)+w(t))/24#

Simplifying we get
#s(t) = (24)/(13) w(t)#

It follows that
#(d s(t))/(dt) = (24)/(13) * (d w(t))/(dt)#

At some particular time #t=T# (we don't really care when) we are told
#(d w(t))/(dt) = 2 (feet)/(sec)# ...or in the diagram #4 (halffeet)/(sec)#

The rate of the shadow's movement is
#(d s(t))/(dt) = (24)/(11) * 2 (feet)/sec)#

#= 4.36 (feet)/(sec)# ...approximately

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