Question

# A ladder $$10m$$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the grough away from the wall at the rate of $$3cm/s$$. The height of the upper end while is is descending at the rate of $$4cm/s$$ is

A
43m
B
53m
C
6m
D
8m

Solution

## The correct option is B $$6m$$Let $$AB=xm, BC=ym$$ and $$AC =10m$$$${ x }^{ 2 }+{ y }^{ 2 }=100$$   ...(i)On differentiating w.r.t. $$x,$$ we get$$\displaystyle 2x\frac { dx }{ dt } +2y\frac { dy }{ dt } =0$$$$\Rightarrow 2x\left( 3 \right) -2y\left( 4 \right) =0$$$$\displaystyle \Rightarrow x=\frac { 4y }{ 3 }$$On putting this value in Eq. (i) we get$$\displaystyle \frac { 16 }{ 9 } { y }^{ 2 }+{ y }^{ 2 }=100$$$$\displaystyle \Rightarrow { y }^{ 2 }=\frac { 100\times 9 }{ 25 } =36\Rightarrow y=6m$$Mathematics

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