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A ladder long rests against a vertical wall If the top of the ladder slides down at a rate of how fast is the bottom of the ladder sliding away when the bottom of the ladder is away from the wall?
Wiki User
∙ 12y ago
If h is vertical height, b=horizontal distance from wall to bottom of ladder and l=lenght of ladder,we can say lsquared = hsquared + b squared.
Now differentiate w.r.t. time t.
2l*dl/dt= 2h* dh/dt + 2b*db/dt =0
However this solution doesn't give exactly the same answer when one solves the problem geometrically or using simple pythagorus.
For example ,if l=20m and b=12 m and h=16m and db/dt is 2m/s, I calculate dh/dt as !.5 m/s using calculus but 1.717 m/s using geometry or straight Pythagorus. Where is the fallasy inthe method using calculus?
Ray Bevan
Wiki User
∙ 12y ago
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