Asked by manjeet
A ladder is intended to reach the wall of a building, but it must clear a fence with the length of d that stands at the distance b from
that wall. Find the shortest length of ladder required to arrange this.
note use differential calculus
that wall. Find the shortest length of ladder required to arrange this.
note use differential calculus
Answers
Answered by
Steve
Draw a diagram. Let
x = length of ladder
z = distance from fence to base of ladder
z/√(b^2+z^2) = (z+d)/x
xz = (z+d)√(b^2+z^2)
x = (z+db^2)√(b^2+z^2)/z
dx/dz = (z^3-db^2)/(z^2 √(b^2+z^2))
dx/dz=0 when z^3 = db^2
Use that to evaluate x
x = length of ladder
z = distance from fence to base of ladder
z/√(b^2+z^2) = (z+d)/x
xz = (z+d)√(b^2+z^2)
x = (z+db^2)√(b^2+z^2)/z
dx/dz = (z^3-db^2)/(z^2 √(b^2+z^2))
dx/dz=0 when z^3 = db^2
Use that to evaluate x
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