A) \[2v\,\text{sin}\,\alpha \]
B) \[2v\cos \alpha \]
C) \[v\sin \alpha \]
D) \[v\cos \alpha \]
Correct Answer: A
Solution :
[a] We resolve the velocity vector \[\vec{v}\] of the person into two components, one parallel to the mirror, \[{{\vec{v}}_{||}}\] and the other perpendicular to the mirror, \[{{\vec{v}}_{\bot }},\]i.e.\[\vec{v}={{\vec{v}}_{||}}+{{\vec{v}}_{\bot }}\] (figure). The velocity of the image will obviously be\[\vec{v}={{\vec{v}}_{||}}-{{\vec{v}}_{\bot }}\] . Therefore the velocity at which the person approaches his image is defined as his velocity relative to the image. From the formula \[{{v}_{rel}}=2{{v}_{\bot }}=2v\sin \alpha .\]You need to login to perform this action.
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