At what rate is the boat approachng the dock when it is 8m from the dock?
Illustration:
Required: dxdt when x=8m
Solution:
By using Pythagorean Theorem we have,
z2=12+x2 Equation 1
taking the derivative with respect to time
\cancel2zdzdt=\cancel2xdxdtdxdt=zxdzdtEquation 2
We can get the value of z by substituting x=8 in equation 1
z2=12+x2z2=12+82z=√65m
Now, using equation 2 to solve for the unknown
dxdt=√658(1)dxdt=√658m/s
This means that the boat is approaching the dock at a rate of √658m/s when the boat is 8m from the dock.
Saturday, January 31, 2015
Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 20
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