Question

A man is moving with constant velocity v₂ = 20m/s in horizontal plane. A what angle to the horizontal should the man hold his umbrella so that the can protect himself from rain falling vertically with velocity 60m/sec.

• A. sin^–1 3
• B. tan^–1 3
• C. cos^–1 3
• D. tan^–1 $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (B)

tan^–1 3

Answer 2

Man should hold the umbrella in direction in which rain appears to come i.e., ${\overset{\rightarrow}{v}}_{rm}$

${\overset{\rightarrow}{v}}_{rm}$= ${\overset{\rightarrow}{v}}_{r}$ – ${\overset{\rightarrow}{v}}_{m}$ ; v_rm ®Velocity of rain with respect to man.

${\overset{\rightarrow}{v}}_{r}$ = ${\overset{\rightarrow}{v}}_{rm}$ + ${\overset{\rightarrow}{v}}_{m}$

tan a = $\frac{v_{r}}{v_{m}}$ = $\frac{60}{20}$ = 3

= tan^–1 3