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Question

A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is
  1. 83
  2. 65
  3. 32
  4. 174


Solution

The correct option is A 83
From figure, x2+y2=400       
Given dydt=2 ft/sec

x2+y2=400 
Differentiate w.r.t t
2xdxdt+2ydydt=0
xdxdt=2y

Now, when x=12y=16
12×dxdt=2×16
dxdt=83

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