A person walking at 4 m/s finds rain drops falling slantwise into his face with a speed of 4 m/s at an angle of `30^(@)` with the vertical . Show that the actual speed of the rain drops is 4 m/s .

Explanation

Velocity of man = 4 m/sec
Apparent velocity of rain drop = 4 m/sec
with `theta = 30^(@)` with vertical . This is relative velocity `V_(B)`
a) Velocity of man `=4hat(i)`
Velocity of rain = 4 m/s , `30^(@)` with vertical
`:.` It is represented by
` = - 4 sin 30 i - 4 , cos 30^(@) hat(j)`
`= - 4 * (1)/(2) hat(i) + 4 (sqrt(3))/(2) say V_(R) = - 2 hat(i) + 2 sqrt(3 )hat(j)`
But `V_(R) = V_(B) - V_(A)` where `V_(B)` is actual velocity of rain
`V_(B)-V_(B)+V_(A)=V_(B)`
` = - 2 hat(i) + 2 sqrt(3)hat(j) + 4 hat(i) = 2 hat(i) + 2 sqrt(3)hat(i)`
`|V_(B)| = sqrt(4 + 4xx3) = sqrt(16) = 4 m//s`