A) \[\frac{\sqrt{2}}{10}\,knot/h\]
B) \[\frac{10}{\sqrt{2}}\,knot/h\]
C) \[10\sqrt{2}\,knot/h\]
D) \[2\sqrt{10}\,knot/h\]
E) \[10\,knot/h\]
Correct Answer: C
Solution :
\[{{({{v}_{rel}})}_{x\to y}}=5\hat{i}-2\hat{j}\] and \[{{({{v}_{rel}})}_{y\to z}}=9\hat{i}+4\hat{j}\] \[\therefore \] \[{{({{v}_{rel}})}_{x\to y}}+{{({{v}_{rel}})}_{y\to z}}\] \[=(5\hat{i}-2\hat{j})+(9\hat{i}+4\hat{j})=14\hat{i}+2\hat{j}\] \[\Rightarrow \] \[|\overrightarrow{v}|=|14\hat{i}+2\hat{j}|=\sqrt{{{14}^{2}}+{{2}^{2}}}\] \[=\sqrt{200}=10\sqrt{2}\,knot/h\]
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