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Calculus/Calculus applying derevitives

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Expert: - 5/17/2008


Question
Here is my problem:

Hauling in a Dinghy: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6ft above the bow. The rope is hauled in at the rate of 2ft/sec.

A. How fast is the boat approaching the dock when 10 ft. of rope are out?

B. At what rate is angle theda changing at that moment?

Answer
A. Note there is a triangle h=height=6' and c=diagonal=rope out=10'.  If b=base, it is known that b^2 + h^2 = c^2.  The variables b and d are really b(t) and c(t) whereas h is a constant (6).  At this point in time, b is known to be 10, so h can be found an put into the equation.

Take the derivative of the equation and know that dc/dt=-2.  Substitute in the values for b and c.  All that's left in the equation is what you are looking for, which should be a negative number.

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