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

- 13
- 43
- 23
- 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=0∴dydt=−xy.dxdt=−x√400−x2.dxdt=−16√400−(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.

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=0∴dydt=−xy.dxdt=−x√400−x2.dxdt=−16√400−(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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