Question

A lamp of negligible height, is placed on the ground '' m away from a wall. A man 'l₂' m tall is walking at a speed of $\frac { \ell _ { 1 } } { 10 }$ m/sec from the lamp to the nearest point on the wall. When he is midway between the lamp and the wall, the rate of change in the length of his shadow on the wall is

• A. $- \frac { 5 \ell _ { 2 } } { 2 } \mathrm {~m} / \mathrm { sec }$
• B. $- \frac { 2 \ell _ { 2 } } { 5 } \mathrm {~m} / \mathrm { sec }$
• C. $- \frac { \ell _ { 2 } } { 2 } \mathrm {~m} / \mathrm { sec }$
• D. $- \frac { \ell _ { 2 } } { 5 } \mathrm {~m} / \mathrm { sec }$

Answer 1

Answer: (B)

$- \frac { 2 \ell _ { 2 } } { 5 } \mathrm {~m} / \mathrm { sec }$

Answer 2

Let BP = x. From similar ∆'s property we get

$\frac { A O } { l _ { 1 } } = \frac { \ell _ { 2 } } { x }$ ⇒ AO = $\frac { \ell _ { 1 } \ell _ { 2 } } { x }$

⇒

when. x = m/sec.