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Question

A ladder 20 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. 13
  2. 43
  3. 23
  4. 53


Solution

The correct option is B 43
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=xy.dxdt=x400x2.dxdt=16400(16)2.dxdt=43dxdt
–ve sign indicates, that when x increases with time, y decreases.
Hence, the supper end is moving 4/3 times as fast as the lower end.

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