Question

Man is running with the speed of 10m/s and finds the rain is falling vertically with speed of 20m/s. At what speed should the man run, such that the rain appear to him, at an angle of ${37}^0$ with vertical.

Answer 1

Given,

The Speed of the man $V_m=10m/s$

The speed of the rain is $V_r=20m/s$

$Angle={37}^0$

${\overrightarrow{V}}_{r}sin\theta ={\overrightarrow{V}}_m$

$20\times sin\theta =10$

$\theta =si{n}^{-1}\frac{1}{2}={30}^0$

Now,

${\overrightarrow{V}}_m=\overrightarrow{V}$

$V_{r}cos{30}^0=R^{-1}cos{37}^0$

Where R is the resultant.

$20\times \frac{\sqrt{3}}{2}=R\times \frac{4}{5}$

$R=\frac{25\sqrt{3}}{2}$

Now,

$V_{r}sin{30}^0=Rsin{37}^0$

$20\times \frac{1}{2}=\frac{25\sqrt{3}}{2}\times \frac{3}{5}$

$V_{rm}=10-\frac{15}{2}\sqrt{3}=\frac{5}{2}\sqrt{3}$