A man 2m tall, walks at the rate of `1 2/3m//s e c` towards a street light which is `5 1/3` m above the ground. At what rate is tip of his shadow moving? At what rate is the length of the shadow changing when he is `3 1/(13)m` from the base of the light?

Explanation

Let AB be the height of lamppost or straight light.
and CD be the height of man at any time t. theman CD is at a distance xm from the straight light. y is the shadow of the man.

`dx/dt=5/3m|s`

`/_ABE and /_CDE` are similar

`(AB)/(CD)=(BE)/(DE)=(AE)/(CE)`

`(15/3)/2=(x+y)/y`

`16/6=(x+y)/y`

`16y-6y=6x`

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