# A man is walking due east at the rate of of 4kmph and the rain is falling 30° east of vertical with a velocity of 6kmph the velocity of rain relative to the man will be?

Jul 30, 2018

${V}_{\text{res" = 5.3 "km"/"hr}}$

#### Explanation:

The vertical component of the rain's velocity is

${V}_{\text{rv" = 6 "km"/"hr"*cos30^@ = 5.2 "km"/"hr}}$

The horizontal component of the rain's velocity is

${V}_{\text{rv" = 6 "km"/"hr"*sin30^@ = 3 "km"/"hr}}$

To the man, the vertical component of the falling rain is $5.2 \text{km"/"hr}$
and the
horizontal component of the falling rain is $\left(4 - 3\right) \text{km"/"hr" = 1 "km"/"hr}$.

To the man, the velocity of the falling rain is the resultant of those 2 velocity components:

${V}_{\text{res" = sqrt(5.2^2 + 1^2) "km"/"hr" = 5.3 "km"/"hr}}$

I hope this helps,
Steve