A man standing under a street lamp of height 'H' above the ground starts running with a constant speed 'v' in a constant direction. The light from the lamp falling on the man forms a shadow of him. Find the velocity with which the edge of the shadow of the man's head moves over the ground if his height is "h".

A man standing under a street lamp of height 'H' above the ground star

1.	A man standing under a street lamp of height 'H' above the ground starts running with a constant speed 'v' in a constant direction. The light from the lamp falling on the man forms a shadow of him. Find the velocity with which the edge of the shadow of the man's head moves over the ground if his height is "h".
Answer» Solution :Here we need to compare the motions of the man and the edge of the shadow of the man's head. To solve this problem, a common starting point is NECESSARY. Let this point be 'O' which is taken exactly under the lamp as shown in the FIGURE. Let 's' and 'S' be the DISTANCE covered in a time interval 't' from the point 'O' by the man and the edge of the shadow of the man's head respectively. As shown in figure we get two similar TRIANGLES namely `DeltaABDandDeltaACO`. From these two similar triangles we get, `(DB)/(AD)=(OC)/(AO),s/(H-h)=S/H` But we know, s = VT `(vt)/(H-h)=S/H` We know that S/t is the speed of the shadow of the man's head, Thus, `V=(Hv)/(H-h)`