AP EAMCET202017 Sep 2020Evening ShiftMathematicsHeights and DistancesActual
A man (2 ~m ) tall, walks at the rate of (1 2 3 ~m / s ) towards a street light which is (5 1 3 ~m ) above the ground. The rate at which the length of his shadow is changing when he is (3 1 3 ~m ) away from the base of the light is ____
Options
- A(-1 ~m / s ⁻¹ )
- B(2 ~m / s )
- C(-2 ~m / s )
- D(1 ~m / s )
Correct answer
A. (-1 ~m / s ⁻¹ )
Step-by-step solution
(A B= ) street light, (C= ) Man. From ( A B E ) and ( D C E ), ( aligned A B C D & = A E C E = A C+C E C E A B C D & = A C C E +1 A C C E = A B C D -1 & A C C E = 5 1 2 2 -1= 5 3 C E= 3 5 A C aligned ) Differentiating with respect to time we get, ( d d t C E= 3 5 ( d d t A C ) (i) ) None ( d d t A C=-1 2 3 ~ms ⁻¹ ) ( d d t A C=- 5 3 ~ms ⁻¹ ) Negative sign as (A C ) decreases with time. substituting in Eq. (i) we get. Rate of change of shadow length (= 3 5 (- 5 3 )=-1 ~ms ⁻¹ )