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Question

A ladder20 ft long has one end on the ground and the other end in contact with a vertical wall. The lower end slips along the ground. If the lower end of the ladder is 16 ft away from the wall, upper end is moving λ  times as fast as the lower end, then λ is 


  1. 2/3

  2. 4/3

  3. 5/3

  4. 1/3


Solution

The correct option is B

4/3


Let OC be the wall. Let AB be the position of the ladder at any time t such that OA =x and OB=y. Length of the ladder AB =20 ft.
In ΔAOB,

x2+y2=(20)2
2xdxdt+2ydydt=0dydt=xydxdt=x400x2.dxdt=16400(16)2.dxdt=43dxdt
-ve sign indicates, that when X increases with time, y decreases. Hence, the upper end is moving 43 times as fast as the lower end.
 

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