Aman of height 2.1 meters walk away from a 5-meter lamppost at a speed of 1.5 m/s. find the rate at which his shadow is increasing in length.

We will draw a diagram showing lamppost and man and then draw vertical lines 5 units and 2 units high respectively and draw horizontal line from lamppost to man then extend it past the man and draw diagonal line from passing through top of vertical lines then extend it until it meets horizontal line. 
suppose d= distance between lamppost and man 
Let s=length of shadow

in given diagram it shows that there are two similar triangles
it shows that smaller triangle has base = s, height = 2 
and larger triangle has base = d+s and height = 5 
by properties of similar triangles 
s/2 = (d+s)/5 
5s = 2d + 2s 
3s = 2d 
s = 2/3 d 
ds/dt = 2/3 dd/dt 
if a man walks at a speed of 1.5 m/s 
dd/dt = 1.5 
ds/dt = 2/3 * 1.5 
ds/dt = 1 
hope it helps

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