Kinematics Question 650
Question: If $ {{\text{V}} _{\text{r}}} $ it’s the velocity of rain falling vertically and $ {{\text{V}} _{\text{m}}} $ it’s the velocity of a man walking on a level road, and $ \theta $ it’s the angle with vertical at which he should hold the umbrella to protect himself than the relative velocity of rain w.r.t. the man it’s 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 _{rm}}=\sqrt{V _{r}^{2}+V _{m}^{2}} $
