A plane mirror is moving with velocity 4hat i | vedclass

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Question

(B) Let the velocity of the object be $\vec{v}_O = 3\hat i + 4\hat j + 5\hat k$ and the velocity of the mirror be $\vec{v}_M = 4\hat i + 5\hat j + 8\h

Vedclass · Accepted Answer

$3\hat i + 4\hat j + 11\hat k$

Vedclass · Answer

(B) Let the velocity of the object be $\vec{v}_O = 3\hat i + 4\hat j + 5\hat k$ and the velocity of the mirror be $\vec{v}_M = 4\hat i + 5\hat j + 8\hat k$.The normal to the mirror is along the $\hat k$ direction.The velocity of the object relative to the mirror is $\vec{v}_{OM} = \vec{v}_O - \vec{v}_M = (3-4)\hat i + (4-5)\hat j + (5-8)\hat k = -\hat i - \hat j - 3\hat k$.For a plane mirror,the component of velocity parallel to the mirror remains unchanged,while the component perpendicular to the mirror (along the normal) reverses sign relative to the mirror.Thus,the velocity of the image relative to the mirror is $\vec{v}_{IM} = -\hat i - \hat j - (-3)\hat k = -\hat i - \hat j + 3\hat k$.Since $\vec{v}_{IM} = \vec{v}_I - \vec{v}_M$,we have $\vec{v}_I = \vec{v}_{IM} + \vec{v}_M$.$\vec{v}_I = (-\hat i - \hat j + 3\hat k) + (4\hat i + 5\hat j + 8\hat k) = 3\hat i + 4\hat j + 11\hat k$.

$A$ plane mirror is moving with velocity $4\hat i + 5\hat j + 8\hat k$. $A$ point object in front of the mirror moves with a velocity $3\hat i + 4\hat j + 5\hat k$. Here,the $\hat k$ direction is along the normal to the plane mirror and facing towards the object. The velocity of the image is:

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