A) 10m
B) \[\frac{7}{\sqrt{2}}\]
C) \[7\sqrt{2}m\]
D) None of these
Correct Answer: C
Solution :
If \[\vec{A}\] is the displacement along the velocity vector, |
then \[\overrightarrow{A}=2\overrightarrow{v}=\left( 6\hat{i}+8\hat{j} \right)\] |
Unit vector along line\[y=x,\] |
\[\overrightarrow{B}=\cos 45{}^\circ \hat{i}+\sin 45{}^\circ \hat{j}\] |
\[=\left( \frac{{\hat{i}}}{\sqrt{2}}+\frac{{\hat{j}}}{\sqrt{2}} \right)\] |
Thus the displacement along \[\overrightarrow{B}\] |
\[A\cos \theta =\frac{AB\cos \theta }{B}=\frac{\overrightarrow{A}.\overrightarrow{B}}{B}\] |
\[^{=}\frac{\left( 6\hat{i}+8\hat{j} \right).\left( \frac{{\hat{i}}}{\sqrt{2}}+\frac{{\hat{j}}}{\sqrt{2}} \right)}{1}\] |
\[=7\sqrt{2}\,\operatorname{m}\] |
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