question_answer

A man of height h walks in a straight path towards a lamp post of height H with uniform velocity u. Then the velocity of the edge of the shadow on the ground will be:

A)  \[\frac{hu}{(H-h)}\]      

B)         \[\frac{Hu}{(H+h)}\]

C)  \[\frac{(H-h)}{Hu}\]      

D)         \[\frac{(H+h)}{Hu}\]

E)  \[\left( \frac{H+h}{H-h} \right)u\]

Correct Answer: A

Solution :

Let in same time t, distance covered by man and edge of image be respectively\[x\]and y. \[\tan \theta =\frac{H-h}{x}=\frac{H}{x+y}\] \[\Rightarrow \]               \[Hx=Hx+Hy-hx+hy\] \[\Rightarrow \]               \[\frac{x}{y}=\frac{(H-h)}{h}\]                   ?. (1) Now   \[x=ut\] and    \[y=vt\] \[\Rightarrow \]               \[\frac{x}{y}=\frac{u}{v}\] Hence,  \[\frac{u}{v}=\frac{(H-h)}{h}\] \[\Rightarrow \]               \[v=\frac{hu}{(H-h)}\]