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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
Answer: A
The shadow is 1.6 m long.
After 4 seconds the object is 1.2 × 4 = 4.8 m from the lamp post. Let the shadow length be x. The lamp, the top of the object and the tip of the shadow lie on one line, so the triangles formed by the lamp post and by the object are similar:
\[ \begin{aligned} \frac{3.6}{4.8 + x} &= \frac{0.9}{x} \\ 3.6x &= 0.9x + 4.32 \\ 2.7x &= 4.32 \\ x &= 1.6\ \text{m} \end{aligned} \]
Check: the lamp is four times as high as the object, so the shadow is one third of the distance walked, 4.8/3 = 1.6 m. 4.8 is the distance walked (and is printed in cm), and 0.9 m is the object's height.
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