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Application Of Derivatives

Question
CBSEENMA12035036
Wired Faculty App

A man of height 2 metres walks at a uniform speed of 5 km/h away from a lamp post which is 6 metres high. Find the rate at which the length of his shadow increases.

Solution

Let AB be the lamp-post and PQ the man, CP be his shadow at time t.
Let AP PC = y. Also AB = 6 m, PQ = 2 m. Now ∆CAB and ∆CPQ are equiangular and hence similar.

therefore space space space space space PC over AC space equals space PQ over AB space space space space space space space rightwards double arrow space space space space space fraction numerator straight y over denominator straight x plus straight y end fraction space equals space 2 over 6 space space space space space or space space space fraction numerator straight y over denominator straight x plus straight y end fraction space equals space 1 third therefore space space space space space space 3 straight y space equals space straight x plus straight y comma space space space space space space space or space space space space 2 straight y space equals space straight x therefore space space space space space space space space space space space space space space space space space straight x space equals space 2 straight y therefore space space space space space space space space space dx over dt space equals space 2 dy over dt But space dx over dt space equals space 5 space km divided by straight h therefore space space space space space 5 space equals space 2 space dy over dt space space space rightwards double arrow space space space space space dy over dt space equals space 5 over 2 km divided by straight h therefore space space space space length space of space the space shadow space increases space at space the space rate space of space 5 over 2 km divided by straight h.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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