A) \[2\sqrt{2}\,m{{s}^{-1}}\] making an angle of \[45{}^\circ \] with the \[+x\] axis
B) \[2\sqrt{2}\,m{{s}^{-1}}\] making an angle of \[135{}^\circ \] with the \[+x\] axis
C) \[4\text{ }m{{s}^{-1}}\] along the \[-x\] axis
D) \[4\text{ }m{{s}^{-1}}\] along the \[+x\] axis
Correct Answer: C
Solution :
Velocity of the object is \[{{\overrightarrow{v}}_{_{0}}}=(2\hat{i}+2\hat{j})m{{s}^{-1}}\] |
\[\therefore \]Speed of object is \[{{v}_{i}}=\sqrt{{{2}^{2}}+{{2}^{2}}}=2\sqrt{2}m{{s}^{-1}}\] |
=speed of the image\[({{v}_{i}})\]. The velocity \[{{\overrightarrow{v}}_{1}}\]of the image will be as shown in fig. the relative velocity of the image with respect to the object is |
\[\Delta \overrightarrow{v}={{\overrightarrow{v }}_{1}}-{{\overrightarrow{v}}_{0}}={{\overrightarrow{v}}_{1}}+(-{{\overrightarrow{v}}_{0}})\] |
\[={{\left[ {{\left( 2\sqrt{2} \right)}^{2}}+{{\left( 2\sqrt{2} \right)}^{2}} \right]}^{1/2}}=4\,m{{s}^{-1}}\,\,along-x\,\,axis.\] |
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