Question

A man walking on a horizontal Road with a speed of 4 kilometre per hour finds that raindrops are hitting his head vertically. When he decreases his speed to 3 kilometre per hour he finds that raindrops are hitting his head at an angle of 30 degree with the vertical. What will be the magnitude of velocity of the raindrops with respect to ground?


A) 3kmph
B)Root 17 kmph
C) Root 19 kmph
D) 3root2 kmph

Answer 1

A) 3kmph is the right answer

Answer 2

velocity of rain, =$\sqrt 19$ km/h

Explanation:

Given,

$V_m = 4i$

let,

$v_r = ai + bj$ km/h

first case,

$V_r_m = V_r - V_m = (a - 4)\times i + bj$

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

so, a - 4 = 0

a = 4

second case,

$V_m = 3$

$V_r_m = i+ bj$ km/h

$\tan30\degree = \frac{1}{\sqrt 3} = \frac{1}{b}$

so,

$b= \sqrt 3$  km/h

velocity of rain, =$\sqrt 19$ km/h