Question

Simple qns :-

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


Explain with diagram
Explanation needed!!​

Answer 1

Answer:

Explanation: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 ΔABDandΔACO. 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

Answer 2

Explanation:

given :

• man standing under a street lamp of height = H

• constant speed v in a constant direction

to find :

• Find the velocity with which the edge of shadow of man's head moves over ground if his height is h = ?

solution :

• speed 1 constant = v 1

• speed 2 constant = v2

then, we will do and we will using y

in this question

• H/(y)=h/(y-x)

• Hy-Hx=hy

• (H-h)y=Hx

• then, we will difference between it we get

• (H-h)v2=Hv

• Hv/(H-h)

• velocity with which the edge of shadow of man's head moves over ground if his height = Hv/(H-h)