Question

Why do we divide 3.1 by 1.25 to get 0.4?
Question 3. http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/units-and-dimensional-analysis/MIT8_01SC_problems01_soln.pdf

Answer 1

The formula for the speed of the boat from dimensional analysis is \[v _{b}=c \sqrt{lg}\] where c is a constant. To find c, the formula given by Rousmaniere, The Annapolis Book of Seamanship, Chapter 1, p35 is given as \[v _{b}=1.25\sqrt{l}\] By equating these, we can solve for c
\[1.25\sqrt{l}=c \sqrt{lg}=3.1c \sqrt{l}\]
\[1.25=3.1c\]
and c =0.40. Now substitute c into the top equation gives\[v _{b}=0.40\sqrt{lg}\]
Note that the info from Rousmaniere is not given in the original question, and hence we cannot solve for c without additional information.

Answer 2

oh ok, thank you so much