Kinematics Question 650
If $ {{\text{V}} _{\text{r}}} $ is the velocity of rain falling vertically and $ {{\text{V}} _{\text{m}}} $ is the velocity of a man walking on a level road, and $ \theta $ is the angle with vertical at which he should hold the umbrella to protect himself, then the relative velocity of rain w.r.t. the man is given by:
Options:
A) $ {{\text{V}} _{\text{r}\text{m}}}=\sqrt{{{V _{r}}^{2}}+{{\text{V}} _{\text{m}}}^{2}+2{{V _{r}}{{\text{V}} _{\text{m}}}\cos \theta }$
B) $ {{\text{V}} _{\text{r}\text{m}}}=\sqrt{{{V _{r}}^{2}}+{{\text{V}} _{\text{m}}}^{2}-2{{V _{r}}{{\text{V}} _{\text{m}}}\cos \theta }} $
C) $ {{\text{V}} _{\text{r}\text{m}}}=\sqrt{{{V _{r}}}^{2}+{{\text{V}} _{\text{m}}}^{2}} $
D) $ {{\text{V}} _{\text{r}\text{m}}}=\sqrt{{{V _{r}}}^{2}-{{\text{V}} _{\text{m}}}^{2}} $
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Answer:
Correct Answer: C
Solution:
According to Pythagoras theorem $ V_{rm}=\sqrt{V_{r}^{2}+V_{m}^{2}} $
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