A) \[2\sqrt{2}\,km/h,{{45}^{0}}\]
B) \[\frac{1}{\sqrt{2}}\,km/h,{{30}^{0}}\]
C) \[2\,km/h,{{0}^{0}}\]
D) \[1\,km/h,{{90}^{0}}\]
Correct Answer: A
Solution :
Velocity of man, \[{{v}_{m}}=2\,km/h\] Velocity of rain, \[{{v}_{r}}=2\,km/h\] Then actual velocity \[{{v}_{rm}}=\sqrt{v_{m}^{2}+v_{r}^{2}}\] \[=\sqrt{{{(2)}^{2}}+{{(2)}^{2}}}\] \[=\sqrt{4+4}=2\sqrt{2}\,km/h\] The direction of rainfall with the vertical \[\sin \theta =\frac{{{v}_{r}}}{{{v}_{rm}}}\] \[=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}\] \[\theta ={{\sin }^{-1}}\left( \frac{1}{\sqrt{2}} \right)\] \[\theta ={{45}^{o}}\]You need to login to perform this action.
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