Question

A plane mirror is moving with velocity $ 4i + 5j + 8k $ . The point object in front of the mirror moves with a velocity $ 3i + 4j + 5k $ . Here $ k $ is along the normal to the plane mirror and facing towards the object. The velocity of the images is:
A. $ - 3i - 4j + 5k $
B. $ 3i + 4j + 11k $
C. $ - 3i - 4j + 11k $
D. $ 7i + 4j + 11k $

Answer 1

Hint: To solve this question, first we will rewrite the given facts given in this question and then we will find the Velocity of Object with respect to mirror. After this, we will conclude the velocity of the image with respect to the mirror. Now we can find the velocity of the image.

Complete step by step solution:
Given that-
Velocity of mirror:
 $ {V_M} = 4i + 5j + 8k $
And, velocity of the object:
 $ {V_O} = 3i + 4j + 5k $
So, the Velocity of Object with respect to mirror:
${V_{O - M}} = (3i + 4j + 5k) - (4i + 5j + 8k) $
$= - i - j - 3k $
Now, $ k $ is along the normal to the plane mirror and facing towards the object, so the $ k $ is in the opposite direction. So, the velocity of image with respect to the mirror:
$ {V_{I - M}} = - i - j + 3k $
As per the rule of image, the velocity of image is:
${V_I} = {V_{I - M}} + {V_M} $
$= ( - i - j + 3k) + (4i + 5j + 8k) $
$= 3i + 4j + 11k $
Therefore, the velocity of the image is $ 3i + 4j + 11k $ .
Hence, the correct option is (B.) $ 3i + 4j + 11k $ .

Note:
An image is the point of convergence or apparent point of divergence of rays after they interact with a given optical element. An object produces rays that will be incident on an optical element.