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Question

A ladder 10 m long against a vertical wall with the lower and on the horizontal ground.

The lower end of the ladder is pulled along the ground away from the wall at the rate of 3cm/sec.

The height of the upper end while it is descending at the rate of 4 cm/sec is


A

43 m

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B

53 m

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C

52 m

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D

8 m

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E

6 m

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Solution

The correct option is E

6 m


The explanation for the correct option:

Step 1: Calculate the third side

Since the given triangle is a right-angle triangle

Using the Pythagorean theorem,

x2+y2=102x2+y2=100

Now,

dxdt=3cm/secdydt=4cm/sec

Step 2: Finding the values of x and y

2x(dxdt)+2y(dydt)=0x(dxdt)+y(dydt)=03x4y=04y=3xx=4y3

Step 3. Put the value of x in x2+y2=100

x2+y2=100(4y3)2+y2=10016y2+9y2=90025y2=900y2=36y=6

Hence, the height of the upper end is 6 m


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