Question

A person observes that rain strikes him normally when he is moving with $2$ kmph. When he reverses his direction and moves with the same speed, the rain will strike him at an angle ${45}^o$ with the vertical. Determine the true velocity of rainfall is?

• A. $2\sqrt{5}$ kmph
• B. $\sqrt{2}$ kmph
• C. $5\sqrt{2}$ kmph
• D. $\sqrt{5}$ kmph

Answer 1

The correct option is A $2\sqrt{5}$ kmph

$V_m=2i$

$\overrightarrow{V_{r,m}}=(a-2)i+b\hat{j}\overrightarrow{V_r}=ai+b\hat{j}\theta =0°\tan \theta =\frac{a-2}{6}=0a=2V_m=-2i\theta =45°\tan 45=\frac{a+2}{b}=\frac{4}{6}b=4\overrightarrow{V_r}=2i+\widehat{4j}\left|V_r\right|=\sqrt{4+16}=2\sqrt{5}m/s$