Q. 124.4( 10 Votes )

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.

Answer :


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


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