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 than the relative velocity of rain w.r.t. the man is given by:

Question

TuteeHUB · Accepted Answer

$${{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}-{{\text{V}}_{\text{m}}}^{2}}$$

TuteeHUB · Answer

$${{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}+2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }$$

TuteeHUB · Answer

$${{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}-2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }$$

TuteeHUB · Answer

$${{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}}$$

1.	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 than the relative velocity of rain w.r.t. the man is given by:
A.	\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}+2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }\]
B.	\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}-2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }\]
C.	\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}}\]
D.	\[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}-{{\text{V}}_{\text{m}}}^{2}}\]
Answer» D. \[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}-{{\text{V}}_{\text{m}}}^{2}}\]

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