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AP EAMCET201922 Apr 2019Morning ShiftMathematicsHeights and DistancesActual

A man of height (2 ~m ) walks at a uniform speed of (7 ~m / min ) away from a lamp post of height (9 ~m ). The rate (( m / min ) ) at which the length of his shadow increases is

Options

  1. A2
  2. B( 5 2 )
  3. C3
  4. D( 7 2 )

Correct answer

A. 2

Step-by-step solution

Let (A B ) be the lamp-post and (P Q ) the man, (C P ) be his shadow at time (t ). Let (A P= ^` x, P C=y ), Also (A B=9 ~m , P Q=2 ~m ) Now, ( C A B ) and ( C P Q ) are equiangular and hence similar. ( aligned & P C A C = P Q A B & y x+y = 2 9 & 9 y=2 x+2 y & 7 y=2 x & x= 7 2 y & d x d t = 7 2 d y d t (differentiating w.r.t. t ) & But d x d t =7 ~m / min & 7= 7 2 d y d t & d y d t =2 ~m / min aligned ) ( ) Length of shadow is increases at (2 ~m / min ).

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