Question

A man of height 2 m walks at a uniform speed of 6 km/hr away from a lamp post of 6 m high. find the rate at which the length of the shadow is increasing.​

Answer 1

Answer:

Let the length of shadow be DE = ym

and let the distance between the man and the lamp post be x meter.

Let AB be the height of the lamp post and CD be the height of man.

∴ AB = 6m and CD = 2m

Therefore, by similar triangles theorem,

AB = CD

BE    DE

  6        = 2

x + y         y

6y = 2x + 2y

⇒x=2y⟶(1)

Differentiating equation (1) w.r.t. time, t, we have

dx = 2dy

dt      dt    

∵ dx    =  6km/hr

    dt

∴ 2dy  =   6

    dt

dy = 3km/hr

dt

The rate at which the length of his shadow increases is 3 km/hr

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