Question

To a man running on incline plane at 5 m/s as shown in figure, rain appears to be falling vertical at 2 m/s. Speed of rain with respect to ground is

• A.
  8 m/s
• B.
  $\sqrt{51}$ m/s
• C.
  $\sqrt{86}$ m/s
• D.
  $\sqrt{41}$ m/s

Answer 1

The correct option is D

$\sqrt{41}$ m/s
${\overrightarrow{V}}_{R,G}$ = ${\overrightarrow{V}}_{R,m}$ - ${\overrightarrow{V}}_{G,m}$ = ${\overrightarrow{V}}_{R,m}$ + ${\overrightarrow{V}}_{m,G}$
${\overrightarrow{V}}_{R,G}$ = -2$\hat{j}$ + (4$\hat{i}$ - 3$\hat{j}$) = 4$\hat{i}$ - 5$\hat{j}$
|${\overrightarrow{V}}_{R,G}$| = $\sqrt{4^2+5^2}$ = $\sqrt{41}$ m/s