Question

A man standing on a road has to hold his umbrella at `30^0` with the vertical to keep the rain away. The throws the umbrella and starts running at 10 km/h. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to a. the road, b. the moving man.

Answer 1

Suppose, the velocity of rain with respect of girl `=V_(RG)`
The velocity of rain with respect to the ground `=V_(RG)`
The velocity of giral with respect to ground
`=V_(Gg) = 10km//hr`.
`{:(vecv_(RG)=vecv_(R)-vecv_(G),,....,,(1)),(vecv_(RG)=vecv_(R)-vecv_(g),,....,,(2)),(vecv_(Gg)=vecv_(G)-vecv_(g),,...,,(3)):}`
On adding equation (1) and equation (3)
`vecv_(RG) +vecv_(Gg) = vecv_(R) - vecv_(g) = vecv_(Rg)`

(a) By traingle `AOB`
`sin30^(@)=(AB)/(OB) = (10)/(V_(Rg))` ltbRgt `V_(Rg) = (10)/(sin 30^(@)) = (10)/(1//2) = 20km//hr`
(b) Now, taking
`(V_(RG))/(V_(Gg)) = cot30^(@)`
`(V_(RG))/(10) = sqrt(3)` or `V_(RG) = 10sqrt(3) Km//hr`