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CBSE Class 12-science Answered

A ladder, which is 13 m in length, is resting against a wall.  A man starts pulling the foot of the ladder away from the wall at the rate of 3 m/s.  Find the rate at which the top of the ladder is sliding when the foot of the ladder is 5 m away from the wall.
Asked by Topperlearning User | 05 Aug, 2014, 01:23: PM
answered-by-expert Expert Answer

Let us take x as the distance covered by foot of the ladder in time ‘t’ and y be height of the top of the ladder at time ‘t’.

From the figure, we can see ABC is a

Right angle triangle

S o comma space A C squared equals A B squared plus B C squared rightwards double arrow y squared plus x squared equals 169  

Differentiating this equations now with respect to t we get

 2 straight y. dy over dt plus 2 straight x. dx over dt equals 0 

This means

dy over dt equals minus straight x over straight y cross times dx over dt

When x = 5 m, y = 12 m

So, dy over dt equals minus 5 over 12 cross times 3 equals minus 5 over 4 straight m divided by straight s

The height of the top of the ladder is decreasing at the rate of 5 over 4 space m divided by s

Answered by | 05 Aug, 2014, 03:23: PM

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