A man is walking on a horizontal road with a speed of 4km/hr finds that raindrops hitting his head vertically. When he decrease his speed to 3km/hr he finds that raindrops are hitting his head at an angle of 30 degrees with the vertical. The magnitude of velocity of the raindrops w.r.t ground will be…

V_{m} = 4i km/h

let V_{r} = ai+bj km/h

first case

V_{rm} =V_{r}-V_{m}= (a-4)i + bj

since rain is falling vertical then velocity along x axis must be zero

so, a-4=0

a=4

second case

V_{m}= 3 km/h

V_{rm}= i+ bj km/h

tan30°=1/√3=1/b

so b= √3 km/h

velocity of rain =√19 km/h