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

Let AB be the lamppost which is 6 m high and CD be the man of height 2 m. EC = x be the shadow and y is the distance covered by man walking away from lamppost at speed of 5 km/h

Hence the rate of change of y with respect to time t is given as 5 km/h that is

Now we have to find the change in x that is length of shadow with respect to time hence we need

Let us first establish some relation between x and y

Consider ΔAEB

From figure AB = 6 m and EB = x + y

Consider ΔDEC

From figure DC = 2 m and EC = x

From (a) and (b)

⇒ 3x = x + y

⇒ y = 2x

Now differentiate with respect to time t as we require

It is given that

Hence the length of shadow increases by 2.5 km/hr