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CBSE Class 12-science Answered

A girl whose height is 160 cm is walking with a speed of 4 m/min away from a lamppost, which is 6.4 m high. Now, her shadow is being formed which is increasing as she moves away. Find out the rate at which the shadow is increasing.
Asked by Topperlearning User | 05 Aug, 2014, 01:49: PM
Expert Answer

Here let us take 'x' be the distance covered by the girl in time t.

Thendx over dt equals 4 space straight m divided by min space     

If 'y' is length of shadow in time 't' min then the rate at which the

Length of shadow is increasing is dy over dt which is required.

 

From the figure it is clear that

AB over DC equals BE over EC which means

fraction numerator 6.4 over denominator 1.6 end fraction equals fraction numerator straight y plus straight x over denominator straight y end fraction
rightwards double arrow 4 straight y equals straight y plus straight x
rightwards double arrow 3 straight y equals straight x

Now differentiating the above equation with respect to it, we get

3 dx over dt equals dy over dt

But it is given, 

dx over dt equals 4 straight m divided by min
dy over dt equals 6 space straight m divided by min

This means that the shadow is increasing at the rate of 12m/min.

Answered by | 05 Aug, 2014, 03:49: PM
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