A cubical room is made of mirrors. An insect | vedclass

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(D) Let the velocity of the insect be $v$ along the diagonal of the floor. The diagonal makes an angle of $45^\circ$ with the adjacent walls.When an o

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$10\sqrt{2} \, cm \, s^{-1}$

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(D) Let the velocity of the insect be $v$ along the diagonal of the floor. The diagonal makes an angle of $45^\circ$ with the adjacent walls.When an object moves with velocity $v$ at an angle $	heta$ with a plane mirror,the velocity of its image component perpendicular to the mirror is $v \sin 	heta$ (towards the mirror) and parallel to the mirror is $v \cos 	heta$.However,for a mirror,the velocity of the image is the reflection of the object's velocity vector. If the insect moves with velocity $v$ at $45^\circ$ to the wall,the component of velocity perpendicular to the wall is $v \sin 45^\circ$. The image moves with the same perpendicular component in the opposite direction.Given that the velocity of the image on the wall mirror is $10 \, cm \, s^{-1}$,this refers to the component of the insect's velocity perpendicular to the mirror,which is $v \sin 45^\circ = 10 \, cm \, s^{-1}$.Thus,$v 	imes \frac{1}{\sqrt{2}} = 10$,which gives $v = 10\sqrt{2} \, cm \, s^{-1}$.Since the ceiling mirror is parallel to the floor,the image of the insect in the ceiling mirror moves with the same velocity as the insect itself,which is $v = 10\sqrt{2} \, cm \, s^{-1}$.

$A$ cubical room is made of mirrors. An insect is moving along the diagonal on the floor such that the velocity of the image of the insect on two adjacent wall mirrors is $10 \, cm \, s^{-1}$. The velocity of the image of the insect in the ceiling mirror is:

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