Question

A cubical roots is formed with six plane mirrors. As insect source along the diagonal of the floor with uniform speed. The velocities of its images is two adjacent walls are $20\sqrt{2}cm/s$. Then the velocity of the image formed by the roof is

• A. $20cm/s$
• B. $40cm/s$
• C. $20\sqrt{2}cm/s$
• D. $100\sqrt{2}cm/s$

Answer 1

Answer: (B)

$40cm/s$

The velocity of the image in the adjacent walls is $20\sqrt{2}\text{cm}\text{.}{\text{s}}^{-1}$.

Therefore,

$V_o.\mathrm{Cos}\left({45}^{\circ }\right)=20\sqrt{2}$

Where, $V_o$ is the velocity of the image formed by the roof.

So,

$V_o=\frac{20\sqrt{2}}{\mathrm{Cos}\left({45}^{\circ }\right)}$

$V_o=\frac{20\sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right)}$

$V_o=20\sqrt{2}\times \sqrt{2}$

$V_o=40\text{cm}\text{.}{\text{s}}^{-1}$