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Question

A ladder is $$2$$m long has lower end on the ground and the other end in contact with a vertical wall. The lower end slips along the ground. If upper end is moving downward at the rate of $$25$$ cm/sec and when upper end of ladder is $$1$$m above the ground, then the rate at which lower end of the ladder is sliding on the ground is?


A
253
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B
223
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C
223
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D
253
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Solution

The correct option is C $$-\dfrac{25}{\sqrt{3}}$$
$$x^2+y^2=4\Rightarrow 2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0\Rightarrow \dfrac{dx}{dt}=-\dfrac{y}{x}\cdot \dfrac{dy}{dt}$$
When upper end is $$1$$m above the ground, $$\dfrac{dx}{dt}=-\dfrac{1}{\sqrt{3}}\cdot 25=-\dfrac{25}{\sqrt{3}}$$ cm/sec.
1246475_1613028_ans_eccb42b2f1f348a1bb69478b693ef13e.png

Mathematics

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