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 isÂ
Answer: Option C
:
C
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=−xydxdt=−x√400−x2.dxdt=−16√400−(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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:
C
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=−xydxdt=−x√400−x2.dxdt=−16√400−(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.
Was this answer helpful ?
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