Question

A cubical room is formed with 6 plane mirrors. An insect moves along diagonal of the floor with uniform speed. The velocity components of its image towards the mirror surface in two adjacent walls are $20\sqrt{2}$ cm/s. Then, the velocity of image formed by the roof is

• A. 20 cm/sec
• B. 40 cm/sec
• C. $20\sqrt{2}$ cm/sec
• D. $10\sqrt{2}$ cm/sec

Answer 1

The correct option is B 40 cm/sec

$\therefore$ $y=\sqrt{2}x$
or $\frac{dy}{dt}=\sqrt{2}\frac{dx}{dt}$



Here, $\frac{dx}{dt}=$ speed of image with respect to mirror
$=20\sqrt{2}$ cm/sec
$\frac{dy}{dt}=\sqrt{2}\left(\frac{dx}{dt}\right)=\sqrt{2}\times 20\sqrt{2}$
= 40 cm/sec
Hence, the correct answer is option (b).

Why this question? Caution: The magnitude of velocity of image will be same as that of object in all mirrors.