An object of height 90 cm is moved away from the base of lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, then the length of the shadow of object after 4 seconds will be

The correct answer is (A) 1.6 m.

• Given Data: Object height $h = 90$$\text{ cm}$ = 0.9$\text{ m}$, lamp height $H = 3.6$$\text{ m}$, speed $v = 1.2$$\text{ m/s}$, time $t = 4$$\text{ s}$.
• Distance Moved: $x = v$$\times$ t = 1.2 $\times$ 4 = 4.8$\text{ m}$.
• Shadow Calculation: Let shadow length be $s$. By similar triangles, $\frac{s}{h}=\frac{s+x}{H}⟹\frac{s}{0.9}=\frac{s+4.8}{3.6}⟹4s=s+4.8⟹3s=4.8⟹s=1.6\text{ m}$$\frac{s}{h}$ = $\frac{s + x}{H}$ $\implies$ $\frac{s}{0.9}$ = $\frac{s + 4.8}{3.6}$ $\implies$ 4s = s + 4.8 $\implies$ 3s = 4.8 $\implies$ s = 1.6$\text{ m}$.