Physics Two Dimensional Motion Question 199
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:
[c] According to Pythagoras theorem $ {V _{r,m}}=\sqrt{V _{r}^{2}+V _{m}^{2}} $
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