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Question

A ladder $$10 $$ metres long rests with one end against a vertical wall, the other end on the floor. The lower end moves away from the wall at the rate of $$2$$ metres/minute. The rate at which the upper end falls when its base is $$6$$ metres away from the wall is.


A
3 metres/min
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B
23 metres/min
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C
32 metres/min
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D
None of these
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Solution

The correct option is D $$\dfrac 32$$ metres/min
Given $$\dfrac {dx}{dt}=2$$ meter/min,  $$\dfrac {dy}{dt}$$ $$=?$$  
In a right angled triangle, we have
$$x^2 + y^2 = 100$$
$$\displaystyle 2x \frac {dx}{dt}+2y\frac {dy}{dt}=0$$
At $$x = 6$$, then $$y = 8$$
$$\Rightarrow \displaystyle 2 \times 6 \times  2 + 2 \times  8 \times \dfrac {dy}{dt}=0$$  
$$\displaystyle \dfrac {dy}{dt}=-\frac {24}{16}=\frac {3}{2}$$ meter/minute
$$\displaystyle \left (\frac {dy}{dt}  \right )_{(6,8)}=-\frac {3}{2}$$ meter/minute    
281985_282413_ans_3434dd1d63f24bb8a56ff68b09ad6aa6.png

Mathematics

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