# A man of height h walks in a straight path towards a lamp post of heiight H with uniform velocity u.

The velocity of the edge of shadow on ground will be.

The answer is $$\frac{hu}{H-h}$$

All I was able to do was draw this measly diagram. It’s an understandably difficult to infer question, if not tough as a whole. Help would be appreciated

Let $$x$$ be the distance of the shadow edge to the post and y the distance of the man to the post. From similar triangles, you could establish $$x/(x-y)=H/h$$. Then, rearrange it to get

$$x = \frac{H}{H-h} y$$

And, take the time derivatives on both sides,

$$x’ = \frac{H}{H-h} y’ =\frac{Hu}{H-h}$$

where $$y’$$ is the velocity of the man, i.e. $$y’=u$$, and $$x’$$ is the velocity of the shadow.

• It’s seems to work, but I am still confused about the final answer you obtained. It’s might be right, perhaps I am being dumb, but could you please elaborate your steps?the part where you said$x’=\frac{h}{H-h}y’$, what does it mean in the context of the question? – Aditya Aug 21 at 13:16
• The velocity is defined as the derivative of distance with respect to time. Since x is the distance of the shadow to the post, $x’$ is its velocity. – Quanto Aug 21 at 13:31

$$\frac{x}{x-y}=\frac{H}{h}$$ $$x=\frac{Hx}{h}-{Hy}{h}$$ $$\frac{x(h-H)}{h}=-\frac{Hy}{h}$$ $$x=\frac{Hy}{H-h}$$ $$x=\frac{Hv}{H-h}$$